id	sid	tid	token	lemma	pos
ejpam-2985	1	1	european	european	PROPN
ejpam-2985	1	2	journal	journal	PROPN
ejpam-2985	1	3	of	of	ADP
ejpam-2985	1	4	pure	pure	ADJ
ejpam-2985	1	5	and	and	CCONJ
ejpam-2985	1	6	applied	apply	VERB
ejpam-2985	1	7	mathematics	mathematic	NOUN
ejpam-2985	1	8	vol	vol	NOUN
ejpam-2985	1	9	.	.	PROPN
ejpam-2985	2	1	10	10	NUM
ejpam-2985	2	2	,	,	PUNCT
ejpam-2985	2	3	no	no	INTJ
ejpam-2985	2	4	.	.	NOUN
ejpam-2985	2	5	3	3	NUM
ejpam-2985	2	6	,	,	PUNCT
ejpam-2985	2	7	2017	2017	NUM
ejpam-2985	2	8	,	,	PUNCT
ejpam-2985	2	9	473	473	NUM
ejpam-2985	2	10	-	-	SYM
ejpam-2985	2	11	487	487	NUM
ejpam-2985	2	12	issn	issn	PROPN
ejpam-2985	2	13	1307	1307	NUM
ejpam-2985	2	14	-	-	SYM
ejpam-2985	2	15	5543	5543	NUM
ejpam-2985	2	16	–	–	PUNCT
ejpam-2985	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2985	2	18	published	publish	VERB
ejpam-2985	2	19	by	by	ADP
ejpam-2985	2	20	new	new	PROPN
ejpam-2985	2	21	york	york	PROPN
ejpam-2985	2	22	business	business	PROPN
ejpam-2985	2	23	global	global	ADJ
ejpam-2985	2	24	common	common	ADJ
ejpam-2985	2	25	fixed	fix	VERB
ejpam-2985	2	26	point	point	NOUN
ejpam-2985	2	27	theorems	theorem	NOUN
ejpam-2985	2	28	for	for	ADP
ejpam-2985	2	29	three	three	NUM
ejpam-2985	2	30	maps	map	NOUN
ejpam-2985	2	31	in	in	ADP
ejpam-2985	2	32	cone	cone	NOUN
ejpam-2985	2	33	pentagonal	pentagonal	ADJ
ejpam-2985	2	34	metric	metric	ADJ
ejpam-2985	2	35	spaces	space	NOUN
ejpam-2985	2	36	abba	abba	PROPN
ejpam-2985	2	37	auwalu1,∗	auwalu1,∗	PROPN
ejpam-2985	2	38	,	,	PUNCT
ejpam-2985	2	39	evren	evren	VERB
ejpam-2985	2	40	hınçal1	hınçal1	PROPN
ejpam-2985	2	41	1	1	NUM
ejpam-2985	2	42	department	department	NOUN
ejpam-2985	2	43	of	of	ADP
ejpam-2985	2	44	mathematics	mathematic	NOUN
ejpam-2985	2	45	,	,	PUNCT
ejpam-2985	2	46	near	near	ADP
ejpam-2985	2	47	east	east	PROPN
ejpam-2985	2	48	university	university	PROPN
ejpam-2985	2	49	,	,	PUNCT
ejpam-2985	2	50	nicosia	nicosia	NOUN
ejpam-2985	2	51	-	-	PUNCT
ejpam-2985	2	52	trnc	trnc	PROPN
ejpam-2985	2	53	,	,	PUNCT
ejpam-2985	2	54	turkey	turkey	NOUN
ejpam-2985	2	55	abstract	abstract	NOUN
ejpam-2985	2	56	.	.	PUNCT
ejpam-2985	3	1	in	in	ADP
ejpam-2985	3	2	this	this	DET
ejpam-2985	3	3	paper	paper	NOUN
ejpam-2985	3	4	,	,	PUNCT
ejpam-2985	3	5	we	we	PRON
ejpam-2985	3	6	prove	prove	VERB
ejpam-2985	3	7	some	some	DET
ejpam-2985	3	8	common	common	ADJ
ejpam-2985	3	9	fixed	fix	VERB
ejpam-2985	3	10	point	point	NOUN
ejpam-2985	3	11	theorems	theorem	NOUN
ejpam-2985	3	12	of	of	ADP
ejpam-2985	3	13	three	three	NUM
ejpam-2985	3	14	self	self	NOUN
ejpam-2985	3	15	mappings	mapping	NOUN
ejpam-2985	3	16	in	in	ADP
ejpam-2985	3	17	non	non	ADJ
ejpam-2985	3	18	-	-	ADJ
ejpam-2985	3	19	normal	normal	ADJ
ejpam-2985	3	20	cone	cone	NOUN
ejpam-2985	3	21	pentagonal	pentagonal	ADJ
ejpam-2985	3	22	metric	metric	ADJ
ejpam-2985	3	23	spaces	space	NOUN
ejpam-2985	3	24	.	.	PUNCT
ejpam-2985	4	1	our	our	PRON
ejpam-2985	4	2	results	result	NOUN
ejpam-2985	4	3	extend	extend	VERB
ejpam-2985	4	4	and	and	CCONJ
ejpam-2985	4	5	improve	improve	VERB
ejpam-2985	4	6	the	the	DET
ejpam-2985	4	7	recent	recent	ADJ
ejpam-2985	4	8	results	result	NOUN
ejpam-2985	4	9	announced	announce	VERB
ejpam-2985	4	10	by	by	ADP
ejpam-2985	4	11	many	many	ADJ
ejpam-2985	4	12	authors	author	NOUN
ejpam-2985	4	13	.	.	PUNCT
ejpam-2985	5	1	2010	2010	NUM
ejpam-2985	5	2	mathematics	mathematic	NOUN
ejpam-2985	5	3	subject	subject	NOUN
ejpam-2985	5	4	classifications	classification	NOUN
ejpam-2985	5	5	:	:	PUNCT
ejpam-2985	5	6	47h10	47h10	NUM
ejpam-2985	5	7	,	,	PUNCT
ejpam-2985	5	8	54h25	54h25	NUM
ejpam-2985	5	9	key	key	ADJ
ejpam-2985	5	10	words	word	NOUN
ejpam-2985	5	11	and	and	CCONJ
ejpam-2985	5	12	phrases	phrase	NOUN
ejpam-2985	5	13	:	:	PUNCT
ejpam-2985	5	14	cone	cone	PROPN
ejpam-2985	5	15	pentagonal	pentagonal	ADJ
ejpam-2985	5	16	metric	metric	ADJ
ejpam-2985	5	17	spaces	space	NOUN
ejpam-2985	5	18	,	,	PUNCT
ejpam-2985	5	19	common	common	ADJ
ejpam-2985	5	20	fixed	fix	VERB
ejpam-2985	5	21	point	point	NOUN
ejpam-2985	5	22	,	,	PUNCT
ejpam-2985	5	23	contraction	contraction	NOUN
ejpam-2985	5	24	mapping	mapping	NOUN
ejpam-2985	5	25	principle	principle	NOUN
ejpam-2985	5	26	,	,	PUNCT
ejpam-2985	5	27	weakly	weakly	ADV
ejpam-2985	5	28	compatible	compatible	ADJ
ejpam-2985	5	29	maps	map	NOUN
ejpam-2985	5	30	1	1	NUM
ejpam-2985	5	31	.	.	PUNCT
ejpam-2985	5	32	introduction	introduction	NOUN
ejpam-2985	5	33	the	the	DET
ejpam-2985	5	34	concept	concept	NOUN
ejpam-2985	5	35	of	of	ADP
ejpam-2985	5	36	metric	metric	ADJ
ejpam-2985	5	37	space	space	NOUN
ejpam-2985	5	38	was	be	AUX
ejpam-2985	5	39	introduced	introduce	VERB
ejpam-2985	5	40	by	by	ADP
ejpam-2985	5	41	fŕechet	fŕechet	PROPN
ejpam-2985	6	1	[	[	X
ejpam-2985	6	2	8	8	NUM
ejpam-2985	6	3	]	]	PUNCT
ejpam-2985	6	4	.	.	PUNCT
ejpam-2985	7	1	let	let	VERB
ejpam-2985	7	2	(	(	PUNCT
ejpam-2985	7	3	x	x	X
ejpam-2985	7	4	,	,	PUNCT
ejpam-2985	7	5	d	d	NOUN
ejpam-2985	7	6	)	)	PUNCT
ejpam-2985	7	7	be	be	AUX
ejpam-2985	7	8	a	a	DET
ejpam-2985	7	9	metric	metric	ADJ
ejpam-2985	7	10	space	space	NOUN
ejpam-2985	7	11	and	and	CCONJ
ejpam-2985	7	12	s	s	VERB
ejpam-2985	7	13	:	:	PUNCT
ejpam-2985	7	14	x	x	SYM
ejpam-2985	7	15	→	→	PUNCT
ejpam-2985	7	16	x	x	PUNCT
ejpam-2985	7	17	be	be	AUX
ejpam-2985	7	18	a	a	DET
ejpam-2985	7	19	mapping	mapping	NOUN
ejpam-2985	7	20	.	.	PUNCT
ejpam-2985	8	1	then	then	ADV
ejpam-2985	8	2	s	s	VERB
ejpam-2985	8	3	is	be	AUX
ejpam-2985	8	4	called	call	VERB
ejpam-2985	8	5	banach	banach	NOUN
ejpam-2985	8	6	contraction	contraction	NOUN
ejpam-2985	8	7	if	if	SCONJ
ejpam-2985	8	8	there	there	PRON
ejpam-2985	8	9	exists	exist	VERB
ejpam-2985	8	10	α	α	PRON
ejpam-2985	8	11	∈	∈	PROPN
ejpam-2985	9	1	[	[	X
ejpam-2985	9	2	0	0	NUM
ejpam-2985	9	3	,	,	PUNCT
ejpam-2985	9	4	1	1	NUM
ejpam-2985	9	5	)	)	PUNCT
ejpam-2985	9	6	such	such	ADJ
ejpam-2985	9	7	that	that	SCONJ
ejpam-2985	9	8	d(sx	d(sx	PROPN
ejpam-2985	9	9	,	,	PUNCT
ejpam-2985	9	10	sy	sy	NOUN
ejpam-2985	9	11	)	)	PUNCT
ejpam-2985	9	12	≤	≤	NOUN
ejpam-2985	9	13	αd(x	αd(x	PUNCT
ejpam-2985	9	14	,	,	PUNCT
ejpam-2985	9	15	y	y	NOUN
ejpam-2985	9	16	)	)	PUNCT
ejpam-2985	9	17	,	,	PUNCT
ejpam-2985	9	18	for	for	ADP
ejpam-2985	9	19	all	all	DET
ejpam-2985	9	20	x	x	NOUN
ejpam-2985	9	21	,	,	PUNCT
ejpam-2985	9	22	y	y	PROPN
ejpam-2985	9	23	∈	∈	PROPN
ejpam-2985	9	24	x.	x.	NOUN
ejpam-2985	9	25	(	(	PUNCT
ejpam-2985	9	26	1	1	X
ejpam-2985	9	27	)	)	PUNCT
ejpam-2985	9	28	banach	banach	NOUN
ejpam-2985	10	1	[	[	X
ejpam-2985	10	2	7	7	X
ejpam-2985	10	3	]	]	PUNCT
ejpam-2985	10	4	proved	prove	VERB
ejpam-2985	10	5	that	that	SCONJ
ejpam-2985	10	6	if	if	SCONJ
ejpam-2985	10	7	x	x	PRON
ejpam-2985	10	8	is	be	AUX
ejpam-2985	10	9	complete	complete	ADJ
ejpam-2985	10	10	,	,	PUNCT
ejpam-2985	10	11	then	then	ADV
ejpam-2985	10	12	every	every	DET
ejpam-2985	10	13	banach	banach	NOUN
ejpam-2985	10	14	contraction	contraction	NOUN
ejpam-2985	10	15	mapping	mapping	NOUN
ejpam-2985	10	16	has	have	VERB
ejpam-2985	10	17	a	a	DET
ejpam-2985	10	18	fixed	fix	VERB
ejpam-2985	10	19	point	point	NOUN
ejpam-2985	10	20	.	.	PUNCT
ejpam-2985	11	1	the	the	DET
ejpam-2985	11	2	mapping	mapping	NOUN
ejpam-2985	11	3	s	s	VERB
ejpam-2985	11	4	is	be	AUX
ejpam-2985	11	5	called	call	VERB
ejpam-2985	11	6	kannan	kannan	PROPN
ejpam-2985	11	7	contraction	contraction	NOUN
ejpam-2985	11	8	if	if	SCONJ
ejpam-2985	11	9	there	there	PRON
ejpam-2985	11	10	exists	exist	VERB
ejpam-2985	11	11	α	α	PRON
ejpam-2985	11	12	∈	∈	PROPN
ejpam-2985	12	1	[	[	X
ejpam-2985	12	2	0	0	NUM
ejpam-2985	12	3	,	,	PUNCT
ejpam-2985	12	4	1/2	1/2	NUM
ejpam-2985	12	5	)	)	PUNCT
ejpam-2985	13	1	such	such	ADJ
ejpam-2985	13	2	that	that	SCONJ
ejpam-2985	13	3	d(sx	d(sx	PROPN
ejpam-2985	13	4	,	,	PUNCT
ejpam-2985	13	5	sy	sy	NOUN
ejpam-2985	13	6	)	)	PUNCT
ejpam-2985	13	7	≤	≤	NOUN
ejpam-2985	13	8	α	α	PROPN
ejpam-2985	13	9	[	[	PUNCT
ejpam-2985	13	10	d(x	d(x	PROPN
ejpam-2985	13	11	,	,	PUNCT
ejpam-2985	13	12	sx	sx	PROPN
ejpam-2985	13	13	)	)	PUNCT
ejpam-2985	13	14	+	+	NUM
ejpam-2985	13	15	d(y	d(y	PROPN
ejpam-2985	13	16	,	,	PUNCT
ejpam-2985	13	17	sy	sy	PROPN
ejpam-2985	13	18	)	)	PUNCT
ejpam-2985	13	19	]	]	PUNCT
ejpam-2985	13	20	,	,	PUNCT
ejpam-2985	13	21	for	for	ADP
ejpam-2985	13	22	all	all	DET
ejpam-2985	13	23	x	x	NOUN
ejpam-2985	13	24	,	,	PUNCT
ejpam-2985	13	25	y	y	PROPN
ejpam-2985	13	26	∈	∈	PROPN
ejpam-2985	13	27	x.	x.	NOUN
ejpam-2985	13	28	(	(	PUNCT
ejpam-2985	13	29	2	2	X
ejpam-2985	13	30	)	)	PUNCT
ejpam-2985	13	31	kannan	kannan	NOUN
ejpam-2985	14	1	[	[	X
ejpam-2985	14	2	14	14	NUM
ejpam-2985	14	3	]	]	PUNCT
ejpam-2985	14	4	proved	prove	VERB
ejpam-2985	14	5	that	that	SCONJ
ejpam-2985	14	6	if	if	SCONJ
ejpam-2985	14	7	x	x	PRON
ejpam-2985	14	8	is	be	AUX
ejpam-2985	14	9	complete	complete	ADJ
ejpam-2985	14	10	,	,	PUNCT
ejpam-2985	14	11	then	then	ADV
ejpam-2985	14	12	every	every	DET
ejpam-2985	14	13	kannan	kannan	PROPN
ejpam-2985	14	14	contraction	contraction	NOUN
ejpam-2985	14	15	has	have	VERB
ejpam-2985	14	16	a	a	DET
ejpam-2985	14	17	fixed	fix	VERB
ejpam-2985	14	18	point	point	NOUN
ejpam-2985	14	19	.	.	PUNCT
ejpam-2985	15	1	he	he	PRON
ejpam-2985	15	2	further	far	ADV
ejpam-2985	15	3	showed	show	VERB
ejpam-2985	15	4	that	that	SCONJ
ejpam-2985	15	5	the	the	DET
ejpam-2985	15	6	conditions	condition	NOUN
ejpam-2985	15	7	(	(	PUNCT
ejpam-2985	15	8	1	1	NUM
ejpam-2985	15	9	)	)	PUNCT
ejpam-2985	15	10	and	and	CCONJ
ejpam-2985	15	11	(	(	PUNCT
ejpam-2985	15	12	2	2	X
ejpam-2985	15	13	)	)	PUNCT
ejpam-2985	15	14	are	be	AUX
ejpam-2985	15	15	independent	independent	ADJ
ejpam-2985	15	16	of	of	ADP
ejpam-2985	15	17	each	each	DET
ejpam-2985	15	18	other	other	ADJ
ejpam-2985	15	19	(	(	PUNCT
ejpam-2985	15	20	see	see	VERB
ejpam-2985	15	21	,	,	PUNCT
ejpam-2985	15	22	[	[	X
ejpam-2985	15	23	14	14	NUM
ejpam-2985	15	24	,	,	PUNCT
ejpam-2985	15	25	15	15	NUM
ejpam-2985	15	26	]	]	NUM
ejpam-2985	15	27	)	)	PUNCT
ejpam-2985	15	28	.	.	PUNCT
ejpam-2985	16	1	the	the	DET
ejpam-2985	16	2	study	study	NOUN
ejpam-2985	16	3	of	of	ADP
ejpam-2985	16	4	existence	existence	NOUN
ejpam-2985	16	5	and	and	CCONJ
ejpam-2985	16	6	uniqueness	uniqueness	NOUN
ejpam-2985	16	7	of	of	ADP
ejpam-2985	16	8	fixed	fix	VERB
ejpam-2985	16	9	points	point	NOUN
ejpam-2985	16	10	of	of	ADP
ejpam-2985	16	11	a	a	DET
ejpam-2985	16	12	mapping	mapping	NOUN
ejpam-2985	16	13	and	and	CCONJ
ejpam-2985	16	14	common	common	ADJ
ejpam-2985	16	15	fixed	fix	VERB
ejpam-2985	16	16	points	point	NOUN
ejpam-2985	16	17	of	of	ADP
ejpam-2985	16	18	two	two	NUM
ejpam-2985	16	19	or	or	CCONJ
ejpam-2985	16	20	more	more	ADJ
ejpam-2985	16	21	mappings	mapping	NOUN
ejpam-2985	16	22	has	have	AUX
ejpam-2985	16	23	become	become	VERB
ejpam-2985	16	24	a	a	DET
ejpam-2985	16	25	subject	subject	NOUN
ejpam-2985	16	26	of	of	ADP
ejpam-2985	16	27	great	great	ADJ
ejpam-2985	16	28	interest	interest	NOUN
ejpam-2985	16	29	.	.	PUNCT
ejpam-2985	17	1	many	many	ADJ
ejpam-2985	17	2	authors	author	NOUN
ejpam-2985	17	3	proved	prove	VERB
ejpam-2985	17	4	the	the	DET
ejpam-2985	17	5	banach	banach	NOUN
ejpam-2985	17	6	contraction	contraction	NOUN
ejpam-2985	17	7	and	and	CCONJ
ejpam-2985	17	8	kannan	kannan	PROPN
ejpam-2985	17	9	contraction	contraction	NOUN
ejpam-2985	17	10	principles	principle	NOUN
ejpam-2985	17	11	in	in	ADP
ejpam-2985	17	12	various	various	ADJ
ejpam-2985	17	13	generalized	generalized	ADJ
ejpam-2985	17	14	metric	metric	ADJ
ejpam-2985	17	15	spaces	space	NOUN
ejpam-2985	17	16	(	(	PUNCT
ejpam-2985	17	17	e.g.	e.g.	ADV
ejpam-2985	17	18	,	,	PUNCT
ejpam-2985	17	19	see	see	VERB
ejpam-2985	17	20	[	[	X
ejpam-2985	17	21	4	4	NUM
ejpam-2985	17	22	,	,	PUNCT
ejpam-2985	17	23	5	5	NUM
ejpam-2985	17	24	,	,	PUNCT
ejpam-2985	17	25	6	6	NUM
ejpam-2985	17	26	,	,	PUNCT
ejpam-2985	17	27	9	9	NUM
ejpam-2985	17	28	,	,	PUNCT
ejpam-2985	17	29	10	10	NUM
ejpam-2985	17	30	,	,	PUNCT
ejpam-2985	17	31	11	11	NUM
ejpam-2985	17	32	,	,	PUNCT
ejpam-2985	17	33	13	13	NUM
ejpam-2985	17	34	,	,	PUNCT
ejpam-2985	17	35	18	18	NUM
ejpam-2985	17	36	]	]	PUNCT
ejpam-2985	17	37	)	)	PUNCT
ejpam-2985	17	38	.	.	PUNCT
ejpam-2985	18	1	long	long	ADJ
ejpam-2985	18	2	-	-	PUNCT
ejpam-2985	18	3	guang	guang	PROPN
ejpam-2985	18	4	and	and	CCONJ
ejpam-2985	18	5	xian	xian	NOUN
ejpam-2985	19	1	[	[	X
ejpam-2985	19	2	11	11	NUM
ejpam-2985	19	3	]	]	PUNCT
ejpam-2985	19	4	introduced	introduce	VERB
ejpam-2985	19	5	the	the	DET
ejpam-2985	19	6	concept	concept	NOUN
ejpam-2985	19	7	of	of	ADP
ejpam-2985	19	8	a	a	DET
ejpam-2985	19	9	cone	cone	NOUN
ejpam-2985	19	10	metric	metric	ADJ
ejpam-2985	19	11	space	space	NOUN
ejpam-2985	19	12	and	and	CCONJ
ejpam-2985	19	13	proved	prove	VERB
ejpam-2985	19	14	some	some	DET
ejpam-2985	19	15	fixed	fix	VERB
ejpam-2985	19	16	point	point	NOUN
ejpam-2985	19	17	theorems	theorem	NOUN
ejpam-2985	19	18	for	for	ADP
ejpam-2985	19	19	contractive	contractive	ADJ
ejpam-2985	19	20	type	type	NOUN
ejpam-2985	19	21	conditions	condition	NOUN
ejpam-2985	19	22	in	in	ADP
ejpam-2985	19	23	cone	cone	NOUN
ejpam-2985	19	24	metric	metric	ADJ
ejpam-2985	19	25	spaces	space	NOUN
ejpam-2985	19	26	.	.	PUNCT
ejpam-2985	20	1	later	later	ADV
ejpam-2985	20	2	on	on	ADP
ejpam-2985	20	3	many	many	ADJ
ejpam-2985	20	4	∗corresponding	∗corresponde	VERB
ejpam-2985	20	5	author	author	NOUN
ejpam-2985	20	6	.	.	PUNCT
ejpam-2985	21	1	email	email	NOUN
ejpam-2985	21	2	addresses	address	NOUN
ejpam-2985	21	3	:	:	PUNCT
ejpam-2985	21	4	abba.auwalu@neu.edu.tr	abba.auwalu@neu.edu.tr	ADV
ejpam-2985	21	5	,	,	PUNCT
ejpam-2985	21	6	abbaauwalu@yahoo.com	abbaauwalu@yahoo.com	X
ejpam-2985	21	7	(	(	PUNCT
ejpam-2985	21	8	a.	a.	NOUN
ejpam-2985	21	9	auwalu	auwalu	PROPN
ejpam-2985	21	10	)	)	PUNCT
ejpam-2985	21	11	,	,	PUNCT
ejpam-2985	21	12	evren.hincal@neu.edu.tr	evren.hincal@neu.edu.tr	PROPN
ejpam-2985	21	13	,	,	PUNCT
ejpam-2985	21	14	evrenhincal@yahoo.co.uk	evrenhincal@yahoo.co.uk	PROPN
ejpam-2985	21	15	(	(	PUNCT
ejpam-2985	21	16	e.	e.	PROPN
ejpam-2985	21	17	hınçal	hınçal	PROPN
ejpam-2985	21	18	)	)	PUNCT
ejpam-2985	21	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2985	22	1	473	473	NUM
ejpam-2985	22	2	c	c	X
ejpam-2985	22	3	©	©	PROPN
ejpam-2985	22	4	2017	2017	NUM
ejpam-2985	22	5	ejpam	ejpam	VERB
ejpam-2985	22	6	all	all	DET
ejpam-2985	22	7	rights	right	NOUN
ejpam-2985	22	8	reserved	reserve	VERB
ejpam-2985	22	9	.	.	PUNCT
ejpam-2985	23	1	a.	a.	PROPN
ejpam-2985	23	2	auwalu	auwalu	PROPN
ejpam-2985	23	3	,	,	PUNCT
ejpam-2985	23	4	e.	e.	PROPN
ejpam-2985	23	5	hınçal	hınçal	PROPN
ejpam-2985	23	6	/	/	SYM
ejpam-2985	23	7	eur	eur	PROPN
ejpam-2985	23	8	.	.	PUNCT
ejpam-2985	24	1	j.	j.	PROPN
ejpam-2985	24	2	pure	pure	PROPN
ejpam-2985	24	3	appl	appl	PROPN
ejpam-2985	24	4	.	.	PROPN
ejpam-2985	24	5	math	math	PROPN
ejpam-2985	24	6	,	,	PUNCT
ejpam-2985	24	7	10	10	NUM
ejpam-2985	24	8	(	(	PUNCT
ejpam-2985	24	9	3	3	NUM
ejpam-2985	24	10	)	)	PUNCT
ejpam-2985	24	11	(	(	PUNCT
ejpam-2985	24	12	2017	2017	NUM
ejpam-2985	24	13	)	)	PUNCT
ejpam-2985	24	14	,	,	PUNCT
ejpam-2985	24	15	473	473	NUM
ejpam-2985	24	16	-	-	SYM
ejpam-2985	24	17	487	487	NUM
ejpam-2985	24	18	474	474	NUM
ejpam-2985	24	19	authors	author	NOUN
ejpam-2985	24	20	have	have	VERB
ejpam-2985	24	21	(	(	PUNCT
ejpam-2985	24	22	for	for	ADP
ejpam-2985	24	23	e.g.	e.g.	ADV
ejpam-2985	24	24	,	,	PUNCT
ejpam-2985	24	25	[	[	X
ejpam-2985	24	26	1	1	NUM
ejpam-2985	24	27	,	,	PUNCT
ejpam-2985	24	28	6	6	NUM
ejpam-2985	24	29	,	,	PUNCT
ejpam-2985	24	30	9	9	NUM
ejpam-2985	24	31	,	,	PUNCT
ejpam-2985	24	32	12	12	NUM
ejpam-2985	24	33	,	,	PUNCT
ejpam-2985	24	34	17	17	NUM
ejpam-2985	24	35	,	,	PUNCT
ejpam-2985	24	36	19	19	NUM
ejpam-2985	24	37	]	]	PUNCT
ejpam-2985	24	38	)	)	PUNCT
ejpam-2985	24	39	proved	prove	VERB
ejpam-2985	24	40	some	some	DET
ejpam-2985	24	41	fixed	fix	VERB
ejpam-2985	24	42	point	point	NOUN
ejpam-2985	24	43	theorems	theorem	NOUN
ejpam-2985	24	44	for	for	ADP
ejpam-2985	24	45	different	different	ADJ
ejpam-2985	24	46	contractive	contractive	ADJ
ejpam-2985	24	47	types	type	NOUN
ejpam-2985	24	48	conditions	condition	NOUN
ejpam-2985	24	49	in	in	ADP
ejpam-2985	24	50	cone	cone	NOUN
ejpam-2985	24	51	metric	metric	ADJ
ejpam-2985	24	52	spaces	space	NOUN
ejpam-2985	24	53	.	.	PUNCT
ejpam-2985	25	1	recently	recently	ADV
ejpam-2985	25	2	,	,	PUNCT
ejpam-2985	25	3	garg	garg	NOUN
ejpam-2985	25	4	and	and	CCONJ
ejpam-2985	25	5	agarwal	agarwal	PROPN
ejpam-2985	26	1	[	[	X
ejpam-2985	26	2	9	9	NUM
ejpam-2985	26	3	]	]	PUNCT
ejpam-2985	26	4	introduced	introduce	VERB
ejpam-2985	26	5	the	the	DET
ejpam-2985	26	6	notion	notion	NOUN
ejpam-2985	26	7	of	of	ADP
ejpam-2985	26	8	cone	cone	NOUN
ejpam-2985	26	9	pentagonal	pentagonal	ADJ
ejpam-2985	26	10	metric	metric	ADJ
ejpam-2985	26	11	space	space	NOUN
ejpam-2985	26	12	and	and	CCONJ
ejpam-2985	26	13	proved	prove	VERB
ejpam-2985	26	14	banach	banach	NOUN
ejpam-2985	26	15	contraction	contraction	NOUN
ejpam-2985	26	16	mapping	mapping	NOUN
ejpam-2985	26	17	principle	principle	NOUN
ejpam-2985	26	18	in	in	ADP
ejpam-2985	26	19	a	a	DET
ejpam-2985	26	20	normal	normal	ADJ
ejpam-2985	26	21	cone	cone	NOUN
ejpam-2985	26	22	pentagonal	pentagonal	ADJ
ejpam-2985	26	23	metric	metric	ADJ
ejpam-2985	26	24	space	space	NOUN
ejpam-2985	26	25	setting	setting	NOUN
ejpam-2985	26	26	.	.	PUNCT
ejpam-2985	27	1	motivated	motivated	ADJ
ejpam-2985	27	2	and	and	CCONJ
ejpam-2985	27	3	inspired	inspire	VERB
ejpam-2985	27	4	by	by	ADP
ejpam-2985	27	5	the	the	DET
ejpam-2985	27	6	results	result	NOUN
ejpam-2985	27	7	of	of	ADP
ejpam-2985	27	8	[	[	X
ejpam-2985	27	9	9	9	NUM
ejpam-2985	27	10	,	,	PUNCT
ejpam-2985	27	11	17	17	NUM
ejpam-2985	27	12	,	,	PUNCT
ejpam-2985	27	13	16	16	NUM
ejpam-2985	27	14	]	]	PUNCT
ejpam-2985	27	15	,	,	PUNCT
ejpam-2985	27	16	it	it	PRON
ejpam-2985	27	17	is	be	AUX
ejpam-2985	27	18	our	our	PRON
ejpam-2985	27	19	purpose	purpose	NOUN
ejpam-2985	27	20	in	in	ADP
ejpam-2985	27	21	this	this	DET
ejpam-2985	27	22	paper	paper	NOUN
ejpam-2985	27	23	to	to	PART
ejpam-2985	27	24	continue	continue	VERB
ejpam-2985	27	25	the	the	DET
ejpam-2985	27	26	study	study	NOUN
ejpam-2985	27	27	of	of	ADP
ejpam-2985	27	28	common	common	ADJ
ejpam-2985	27	29	fixed	fix	VERB
ejpam-2985	27	30	points	point	NOUN
ejpam-2985	27	31	of	of	ADP
ejpam-2985	27	32	a	a	DET
ejpam-2985	27	33	three	three	NUM
ejpam-2985	27	34	self	self	NOUN
ejpam-2985	27	35	mappings	mapping	NOUN
ejpam-2985	27	36	in	in	ADP
ejpam-2985	27	37	non	non	ADJ
ejpam-2985	27	38	-	-	ADJ
ejpam-2985	27	39	normal	normal	ADJ
ejpam-2985	27	40	cone	cone	NOUN
ejpam-2985	27	41	pentagonal	pentagonal	ADJ
ejpam-2985	27	42	metric	metric	ADJ
ejpam-2985	27	43	space	space	NOUN
ejpam-2985	27	44	setting	setting	NOUN
ejpam-2985	27	45	.	.	PUNCT
ejpam-2985	28	1	our	our	PRON
ejpam-2985	28	2	results	result	NOUN
ejpam-2985	28	3	extend	extend	VERB
ejpam-2985	28	4	and	and	CCONJ
ejpam-2985	28	5	improve	improve	VERB
ejpam-2985	28	6	the	the	DET
ejpam-2985	28	7	results	result	NOUN
ejpam-2985	28	8	of	of	ADP
ejpam-2985	28	9	[	[	X
ejpam-2985	28	10	2	2	NUM
ejpam-2985	28	11	,	,	PUNCT
ejpam-2985	28	12	3	3	NUM
ejpam-2985	28	13	,	,	PUNCT
ejpam-2985	28	14	6	6	NUM
ejpam-2985	28	15	,	,	PUNCT
ejpam-2985	28	16	9	9	NUM
ejpam-2985	28	17	,	,	PUNCT
ejpam-2985	28	18	13	13	NUM
ejpam-2985	28	19	,	,	PUNCT
ejpam-2985	28	20	18	18	NUM
ejpam-2985	28	21	,	,	PUNCT
ejpam-2985	28	22	17	17	NUM
ejpam-2985	28	23	,	,	PUNCT
ejpam-2985	28	24	16	16	NUM
ejpam-2985	28	25	]	]	PUNCT
ejpam-2985	28	26	,	,	PUNCT
ejpam-2985	28	27	and	and	CCONJ
ejpam-2985	28	28	many	many	ADJ
ejpam-2985	28	29	others	other	NOUN
ejpam-2985	28	30	.	.	PUNCT
ejpam-2985	29	1	2	2	X
ejpam-2985	29	2	.	.	NUM
ejpam-2985	29	3	preliminaries	preliminary	NOUN
ejpam-2985	29	4	the	the	DET
ejpam-2985	29	5	following	follow	VERB
ejpam-2985	29	6	definitions	definition	NOUN
ejpam-2985	29	7	and	and	CCONJ
ejpam-2985	29	8	lemmas	lemma	NOUN
ejpam-2985	29	9	,	,	PUNCT
ejpam-2985	29	10	introduced	introduce	VERB
ejpam-2985	29	11	in	in	ADP
ejpam-2985	29	12	[	[	X
ejpam-2985	29	13	1	1	NUM
ejpam-2985	29	14	,	,	PUNCT
ejpam-2985	29	15	3	3	NUM
ejpam-2985	29	16	,	,	PUNCT
ejpam-2985	29	17	6	6	NUM
ejpam-2985	29	18	,	,	PUNCT
ejpam-2985	29	19	9	9	NUM
ejpam-2985	29	20	,	,	PUNCT
ejpam-2985	29	21	11	11	NUM
ejpam-2985	29	22	]	]	PUNCT
ejpam-2985	29	23	,	,	PUNCT
ejpam-2985	29	24	are	be	AUX
ejpam-2985	29	25	needed	need	VERB
ejpam-2985	29	26	in	in	ADP
ejpam-2985	29	27	the	the	DET
ejpam-2985	29	28	sequel	sequel	NOUN
ejpam-2985	29	29	.	.	PUNCT
ejpam-2985	30	1	definition	definition	NOUN
ejpam-2985	30	2	1	1	NUM
ejpam-2985	30	3	.	.	PUNCT
ejpam-2985	31	1	let	let	VERB
ejpam-2985	31	2	e	e	PRON
ejpam-2985	31	3	be	be	AUX
ejpam-2985	31	4	a	a	DET
ejpam-2985	31	5	real	real	ADJ
ejpam-2985	31	6	banach	banach	NOUN
ejpam-2985	31	7	space	space	NOUN
ejpam-2985	31	8	and	and	CCONJ
ejpam-2985	31	9	p	p	NOUN
ejpam-2985	31	10	subset	subset	NOUN
ejpam-2985	31	11	of	of	ADP
ejpam-2985	31	12	e.	e.	PROPN
ejpam-2985	31	13	p	p	PROPN
ejpam-2985	31	14	is	be	AUX
ejpam-2985	31	15	called	call	VERB
ejpam-2985	31	16	a	a	DET
ejpam-2985	31	17	cone	cone	NOUN
ejpam-2985	31	18	if	if	SCONJ
ejpam-2985	31	19	and	and	CCONJ
ejpam-2985	31	20	only	only	ADV
ejpam-2985	31	21	if	if	SCONJ
ejpam-2985	31	22	:	:	PUNCT
ejpam-2985	31	23	(	(	PUNCT
ejpam-2985	31	24	i	i	NOUN
ejpam-2985	31	25	)	)	PUNCT
ejpam-2985	31	26	p	p	NOUN
ejpam-2985	31	27	is	be	AUX
ejpam-2985	31	28	closed	closed	ADJ
ejpam-2985	31	29	,	,	PUNCT
ejpam-2985	31	30	nonempty	nonempty	NOUN
ejpam-2985	31	31	,	,	PUNCT
ejpam-2985	31	32	and	and	CCONJ
ejpam-2985	31	33	p	p	X
ejpam-2985	31	34	6=	6=	PROPN
ejpam-2985	31	35	{	{	PUNCT
ejpam-2985	31	36	0	0	NUM
ejpam-2985	31	37	}	}	PUNCT
ejpam-2985	31	38	;	;	PUNCT
ejpam-2985	31	39	(	(	PUNCT
ejpam-2985	31	40	ii	ii	NOUN
ejpam-2985	31	41	)	)	PUNCT
ejpam-2985	31	42	a	a	PROPN
ejpam-2985	31	43	,	,	PUNCT
ejpam-2985	31	44	b	b	X
ejpam-2985	31	45	∈	∈	PROPN
ejpam-2985	31	46	r	r	NOUN
ejpam-2985	31	47	,	,	PUNCT
ejpam-2985	31	48	a	a	PRON
ejpam-2985	31	49	,	,	PUNCT
ejpam-2985	31	50	b	b	NOUN
ejpam-2985	31	51	≥	≥	NOUN
ejpam-2985	31	52	0	0	NUM
ejpam-2985	31	53	and	and	CCONJ
ejpam-2985	31	54	x	x	NOUN
ejpam-2985	31	55	,	,	PUNCT
ejpam-2985	31	56	y	y	PROPN
ejpam-2985	31	57	∈	∈	PROPN
ejpam-2985	32	1	p	p	NOUN
ejpam-2985	32	2	=	=	NOUN
ejpam-2985	32	3	⇒	⇒	NOUN
ejpam-2985	32	4	ax+	ax+	NOUN
ejpam-2985	32	5	by	by	ADP
ejpam-2985	32	6	∈	∈	PROPN
ejpam-2985	32	7	p	p	NOUN
ejpam-2985	32	8	;	;	PUNCT
ejpam-2985	32	9	(	(	PUNCT
ejpam-2985	32	10	iii	iii	X
ejpam-2985	32	11	)	)	PUNCT
ejpam-2985	32	12	x	x	SYM
ejpam-2985	32	13	∈	∈	PROPN
ejpam-2985	32	14	p	p	NOUN
ejpam-2985	32	15	and	and	CCONJ
ejpam-2985	32	16	−x	−x	NUM
ejpam-2985	32	17	∈	∈	PROPN
ejpam-2985	32	18	p	p	NOUN
ejpam-2985	32	19	=	=	NOUN
ejpam-2985	32	20	⇒	⇒	NOUN
ejpam-2985	32	21	x	x	PUNCT
ejpam-2985	32	22	=	=	SYM
ejpam-2985	32	23	0	0	NUM
ejpam-2985	32	24	.	.	PUNCT
ejpam-2985	32	25	given	give	VERB
ejpam-2985	32	26	a	a	DET
ejpam-2985	32	27	cone	cone	NOUN
ejpam-2985	32	28	p	p	NOUN
ejpam-2985	32	29	⊆	⊆	NUM
ejpam-2985	32	30	e	e	NOUN
ejpam-2985	32	31	,	,	PUNCT
ejpam-2985	32	32	we	we	PRON
ejpam-2985	32	33	defined	define	VERB
ejpam-2985	32	34	a	a	DET
ejpam-2985	32	35	partial	partial	ADJ
ejpam-2985	32	36	ordering	ordering	NOUN
ejpam-2985	32	37	≤	≤	NOUN
ejpam-2985	32	38	with	with	ADP
ejpam-2985	32	39	respect	respect	NOUN
ejpam-2985	32	40	to	to	ADP
ejpam-2985	32	41	p	p	NOUN
ejpam-2985	32	42	by	by	ADP
ejpam-2985	32	43	x	x	PROPN
ejpam-2985	32	44	≤	≤	NUM
ejpam-2985	32	45	y	y	NOUN
ejpam-2985	32	46	if	if	SCONJ
ejpam-2985	33	1	and	and	CCONJ
ejpam-2985	33	2	only	only	ADV
ejpam-2985	33	3	if	if	SCONJ
ejpam-2985	33	4	y−	y−	NOUN
ejpam-2985	33	5	x	x	SYM
ejpam-2985	33	6	∈	∈	PROPN
ejpam-2985	33	7	p.	p.	NOUN
ejpam-2985	33	8	we	we	PRON
ejpam-2985	33	9	shall	shall	AUX
ejpam-2985	33	10	write	write	VERB
ejpam-2985	33	11	x	x	PUNCT
ejpam-2985	33	12	<	<	X
ejpam-2985	33	13	y	y	X
ejpam-2985	33	14	to	to	PART
ejpam-2985	33	15	indicate	indicate	VERB
ejpam-2985	33	16	that	that	SCONJ
ejpam-2985	33	17	x	x	SYM
ejpam-2985	33	18	≤	≤	ADJ
ejpam-2985	33	19	y	y	PROPN
ejpam-2985	33	20	but	but	CCONJ
ejpam-2985	33	21	x	x	SYM
ejpam-2985	33	22	6=	6=	NUM
ejpam-2985	33	23	y	y	PROPN
ejpam-2985	33	24	,	,	PUNCT
ejpam-2985	33	25	while	while	SCONJ
ejpam-2985	33	26	x	x	X
ejpam-2985	33	27	�	�	PROPN
ejpam-2985	33	28	y	y	PROPN
ejpam-2985	33	29	will	will	AUX
ejpam-2985	33	30	stand	stand	VERB
ejpam-2985	33	31	for	for	ADP
ejpam-2985	33	32	y	y	PROPN
ejpam-2985	33	33	−	−	PROPN
ejpam-2985	33	34	x	x	SYM
ejpam-2985	33	35	∈	∈	PROPN
ejpam-2985	33	36	int(p	int(p	PROPN
ejpam-2985	33	37	)	)	PUNCT
ejpam-2985	33	38	,	,	PUNCT
ejpam-2985	33	39	where	where	SCONJ
ejpam-2985	33	40	int(p	int(p	PROPN
ejpam-2985	33	41	)	)	PUNCT
ejpam-2985	33	42	denotes	denote	VERB
ejpam-2985	33	43	the	the	DET
ejpam-2985	33	44	interior	interior	NOUN
ejpam-2985	33	45	of	of	ADP
ejpam-2985	33	46	p.	p.	PROPN
ejpam-2985	33	47	a	a	DET
ejpam-2985	33	48	cone	cone	NOUN
ejpam-2985	33	49	p	p	NOUN
ejpam-2985	33	50	is	be	AUX
ejpam-2985	33	51	called	call	VERB
ejpam-2985	33	52	normal	normal	ADJ
ejpam-2985	33	53	if	if	SCONJ
ejpam-2985	33	54	there	there	PRON
ejpam-2985	33	55	is	be	VERB
ejpam-2985	33	56	a	a	DET
ejpam-2985	33	57	number	number	NOUN
ejpam-2985	33	58	k	k	PROPN
ejpam-2985	33	59	≥	≥	NUM
ejpam-2985	33	60	1	1	NUM
ejpam-2985	33	61	such	such	ADJ
ejpam-2985	33	62	that	that	PRON
ejpam-2985	33	63	for	for	SCONJ
ejpam-2985	33	64	all	all	DET
ejpam-2985	33	65	x	x	NOUN
ejpam-2985	33	66	,	,	PUNCT
ejpam-2985	33	67	y	y	PROPN
ejpam-2985	33	68	∈	∈	PROPN
ejpam-2985	33	69	e	e	NOUN
ejpam-2985	33	70	,	,	PUNCT
ejpam-2985	33	71	the	the	DET
ejpam-2985	33	72	inequality	inequality	NOUN
ejpam-2985	33	73	0	0	NUM
ejpam-2985	33	74	≤	≤	NUM
ejpam-2985	33	75	x	x	PUNCT
ejpam-2985	33	76	≤	≤	NUM
ejpam-2985	33	77	y	y	NOUN
ejpam-2985	33	78	=	=	NOUN
ejpam-2985	33	79	⇒	⇒	NOUN
ejpam-2985	33	80	‖x‖	‖x‖	PROPN
ejpam-2985	33	81	≤	≤	PROPN
ejpam-2985	33	82	k‖y‖.	k‖y‖.	PUNCT
ejpam-2985	33	83	(	(	PUNCT
ejpam-2985	33	84	3	3	X
ejpam-2985	33	85	)	)	PUNCT
ejpam-2985	33	86	the	the	DET
ejpam-2985	33	87	least	least	ADV
ejpam-2985	33	88	positive	positive	ADJ
ejpam-2985	33	89	number	number	NOUN
ejpam-2985	33	90	k	k	NOUN
ejpam-2985	33	91	satisfying	satisfying	ADJ
ejpam-2985	33	92	(	(	PUNCT
ejpam-2985	33	93	3	3	X
ejpam-2985	33	94	)	)	PUNCT
ejpam-2985	33	95	is	be	AUX
ejpam-2985	33	96	called	call	VERB
ejpam-2985	33	97	the	the	DET
ejpam-2985	33	98	normal	normal	ADJ
ejpam-2985	33	99	constant	constant	NOUN
ejpam-2985	33	100	of	of	ADP
ejpam-2985	33	101	p.	p.	NOUN
ejpam-2985	33	102	in	in	ADP
ejpam-2985	33	103	this	this	DET
ejpam-2985	33	104	paper	paper	NOUN
ejpam-2985	33	105	,	,	PUNCT
ejpam-2985	33	106	we	we	PRON
ejpam-2985	33	107	always	always	ADV
ejpam-2985	33	108	suppose	suppose	VERB
ejpam-2985	33	109	that	that	SCONJ
ejpam-2985	33	110	e	e	PROPN
ejpam-2985	33	111	is	be	AUX
ejpam-2985	33	112	a	a	DET
ejpam-2985	33	113	real	real	ADJ
ejpam-2985	33	114	banach	banach	NOUN
ejpam-2985	33	115	space	space	NOUN
ejpam-2985	33	116	and	and	CCONJ
ejpam-2985	33	117	p	p	NOUN
ejpam-2985	33	118	is	be	AUX
ejpam-2985	33	119	a	a	DET
ejpam-2985	33	120	cone	cone	NOUN
ejpam-2985	33	121	in	in	ADP
ejpam-2985	33	122	e	e	PROPN
ejpam-2985	33	123	with	with	ADP
ejpam-2985	33	124	int(p	int(p	PROPN
ejpam-2985	33	125	)	)	PUNCT
ejpam-2985	33	126	6=	6=	ADP
ejpam-2985	33	127	∅	∅	NOUN
ejpam-2985	33	128	and	and	CCONJ
ejpam-2985	33	129	≤	≤	NOUN
ejpam-2985	33	130	is	be	AUX
ejpam-2985	33	131	a	a	DET
ejpam-2985	33	132	partial	partial	ADJ
ejpam-2985	33	133	ordering	ordering	NOUN
ejpam-2985	33	134	with	with	ADP
ejpam-2985	33	135	respect	respect	NOUN
ejpam-2985	33	136	to	to	ADP
ejpam-2985	33	137	p.	p.	NOUN
ejpam-2985	33	138	definition	definition	NOUN
ejpam-2985	34	1	2	2	X
ejpam-2985	34	2	.	.	PUNCT
ejpam-2985	35	1	let	let	VERB
ejpam-2985	35	2	x	x	PRON
ejpam-2985	35	3	be	be	AUX
ejpam-2985	35	4	a	a	DET
ejpam-2985	35	5	nonempty	nonempty	ADJ
ejpam-2985	35	6	set	set	VERB
ejpam-2985	35	7	.	.	PUNCT
ejpam-2985	36	1	suppose	suppose	VERB
ejpam-2985	36	2	the	the	DET
ejpam-2985	36	3	mapping	mapping	NOUN
ejpam-2985	36	4	ρ	ρ	NOUN
ejpam-2985	36	5	:	:	PUNCT
ejpam-2985	36	6	x	x	X
ejpam-2985	36	7	×x	×x	X
ejpam-2985	36	8	→	→	SYM
ejpam-2985	36	9	e	e	NOUN
ejpam-2985	36	10	satisfies	satisfie	NOUN
ejpam-2985	36	11	:	:	PUNCT
ejpam-2985	36	12	(	(	PUNCT
ejpam-2985	36	13	i	i	NOUN
ejpam-2985	36	14	)	)	PUNCT
ejpam-2985	36	15	0	0	PUNCT
ejpam-2985	37	1	<	<	X
ejpam-2985	37	2	ρ(x	ρ(x	PROPN
ejpam-2985	37	3	,	,	PUNCT
ejpam-2985	37	4	y	y	NOUN
ejpam-2985	37	5	)	)	PUNCT
ejpam-2985	37	6	for	for	ADP
ejpam-2985	37	7	all	all	DET
ejpam-2985	37	8	x	x	NOUN
ejpam-2985	37	9	,	,	PUNCT
ejpam-2985	37	10	y	y	PROPN
ejpam-2985	37	11	∈	∈	PROPN
ejpam-2985	37	12	x	x	X
ejpam-2985	37	13	and	and	CCONJ
ejpam-2985	37	14	ρ(x	ρ(x	PROPN
ejpam-2985	37	15	,	,	PUNCT
ejpam-2985	37	16	y	y	NOUN
ejpam-2985	37	17	)	)	PUNCT
ejpam-2985	37	18	=	=	SYM
ejpam-2985	37	19	0	0	PUNCT
ejpam-2985	38	1	if	if	SCONJ
ejpam-2985	38	2	and	and	CCONJ
ejpam-2985	38	3	only	only	ADV
ejpam-2985	38	4	if	if	SCONJ
ejpam-2985	38	5	x	x	X
ejpam-2985	38	6	=	=	SYM
ejpam-2985	38	7	y	y	PROPN
ejpam-2985	38	8	;	;	PUNCT
ejpam-2985	38	9	(	(	PUNCT
ejpam-2985	38	10	ii	ii	NOUN
ejpam-2985	38	11	)	)	PUNCT
ejpam-2985	38	12	ρ(x	ρ(x	PROPN
ejpam-2985	38	13	,	,	PUNCT
ejpam-2985	38	14	y	y	NOUN
ejpam-2985	38	15	)	)	PUNCT
ejpam-2985	38	16	=	=	SYM
ejpam-2985	38	17	ρ(y	ρ(y	NOUN
ejpam-2985	38	18	,	,	PUNCT
ejpam-2985	38	19	x	x	NOUN
ejpam-2985	38	20	)	)	PUNCT
ejpam-2985	38	21	for	for	ADP
ejpam-2985	38	22	all	all	DET
ejpam-2985	38	23	x	x	NOUN
ejpam-2985	38	24	,	,	PUNCT
ejpam-2985	38	25	y	y	PROPN
ejpam-2985	38	26	∈	∈	PROPN
ejpam-2985	38	27	x	x	X
ejpam-2985	38	28	;	;	PUNCT
ejpam-2985	38	29	(	(	PUNCT
ejpam-2985	38	30	iii	iii	NOUN
ejpam-2985	38	31	)	)	PUNCT
ejpam-2985	38	32	ρ(x	ρ(x	PROPN
ejpam-2985	38	33	,	,	PUNCT
ejpam-2985	38	34	y	y	NOUN
ejpam-2985	38	35	)	)	PUNCT
ejpam-2985	38	36	≤	≤	NOUN
ejpam-2985	38	37	ρ(x	ρ(x	NOUN
ejpam-2985	38	38	,	,	PUNCT
ejpam-2985	38	39	z	z	NOUN
ejpam-2985	38	40	)	)	PUNCT
ejpam-2985	38	41	+	+	CCONJ
ejpam-2985	38	42	ρ(z	ρ(z	PROPN
ejpam-2985	38	43	,	,	PUNCT
ejpam-2985	38	44	y	y	NOUN
ejpam-2985	38	45	)	)	PUNCT
ejpam-2985	38	46	for	for	ADP
ejpam-2985	38	47	all	all	DET
ejpam-2985	38	48	x	x	NOUN
ejpam-2985	38	49	,	,	PUNCT
ejpam-2985	38	50	y	y	PROPN
ejpam-2985	38	51	,	,	PUNCT
ejpam-2985	38	52	z	z	PROPN
ejpam-2985	38	53	∈	∈	PROPN
ejpam-2985	38	54	x.	x.	NOUN
ejpam-2985	38	55	then	then	ADV
ejpam-2985	38	56	ρ	ρ	PROPN
ejpam-2985	38	57	is	be	AUX
ejpam-2985	38	58	called	call	VERB
ejpam-2985	38	59	a	a	DET
ejpam-2985	38	60	cone	cone	NOUN
ejpam-2985	38	61	metric	metric	NOUN
ejpam-2985	38	62	on	on	ADP
ejpam-2985	38	63	x	x	PRON
ejpam-2985	38	64	,	,	PUNCT
ejpam-2985	38	65	and	and	CCONJ
ejpam-2985	38	66	(	(	PUNCT
ejpam-2985	38	67	x	x	X
ejpam-2985	38	68	,	,	PUNCT
ejpam-2985	38	69	ρ	ρ	PROPN
ejpam-2985	38	70	)	)	PUNCT
ejpam-2985	38	71	is	be	AUX
ejpam-2985	38	72	called	call	VERB
ejpam-2985	38	73	a	a	DET
ejpam-2985	38	74	cone	cone	NOUN
ejpam-2985	38	75	metric	metric	ADJ
ejpam-2985	38	76	space	space	NOUN
ejpam-2985	38	77	.	.	PUNCT
ejpam-2985	39	1	the	the	DET
ejpam-2985	39	2	concept	concept	NOUN
ejpam-2985	39	3	of	of	ADP
ejpam-2985	39	4	a	a	DET
ejpam-2985	39	5	cone	cone	NOUN
ejpam-2985	39	6	metric	metric	ADJ
ejpam-2985	39	7	space	space	NOUN
ejpam-2985	39	8	is	be	AUX
ejpam-2985	39	9	more	more	ADV
ejpam-2985	39	10	general	general	ADJ
ejpam-2985	39	11	than	than	ADP
ejpam-2985	39	12	that	that	PRON
ejpam-2985	39	13	of	of	ADP
ejpam-2985	39	14	a	a	DET
ejpam-2985	39	15	metric	metric	ADJ
ejpam-2985	39	16	space	space	NOUN
ejpam-2985	39	17	,	,	PUNCT
ejpam-2985	39	18	because	because	SCONJ
ejpam-2985	39	19	each	each	DET
ejpam-2985	39	20	metric	metric	ADJ
ejpam-2985	39	21	space	space	NOUN
ejpam-2985	39	22	is	be	AUX
ejpam-2985	39	23	a	a	DET
ejpam-2985	39	24	cone	cone	NOUN
ejpam-2985	39	25	metric	metric	ADJ
ejpam-2985	39	26	space	space	NOUN
ejpam-2985	39	27	where	where	SCONJ
ejpam-2985	39	28	e	e	NOUN
ejpam-2985	39	29	=	=	SYM
ejpam-2985	39	30	r	r	NOUN
ejpam-2985	39	31	and	and	CCONJ
ejpam-2985	39	32	p	p	NOUN
ejpam-2985	39	33	=	=	X
ejpam-2985	40	1	[	[	X
ejpam-2985	40	2	0,∞	0,∞	NUM
ejpam-2985	40	3	)	)	PUNCT
ejpam-2985	40	4	(	(	PUNCT
ejpam-2985	40	5	e.g.	e.g.	ADV
ejpam-2985	40	6	,	,	PUNCT
ejpam-2985	40	7	see	see	VERB
ejpam-2985	40	8	[	[	X
ejpam-2985	40	9	11	11	NUM
ejpam-2985	40	10	]	]	NUM
ejpam-2985	40	11	)	)	PUNCT
ejpam-2985	40	12	.	.	PUNCT
ejpam-2985	41	1	a.	a.	PROPN
ejpam-2985	41	2	auwalu	auwalu	PROPN
ejpam-2985	41	3	,	,	PUNCT
ejpam-2985	41	4	e.	e.	PROPN
ejpam-2985	41	5	hınçal	hınçal	PROPN
ejpam-2985	41	6	/	/	SYM
ejpam-2985	41	7	eur	eur	PROPN
ejpam-2985	41	8	.	.	PUNCT
ejpam-2985	42	1	j.	j.	PROPN
ejpam-2985	42	2	pure	pure	PROPN
ejpam-2985	42	3	appl	appl	PROPN
ejpam-2985	42	4	.	.	PROPN
ejpam-2985	42	5	math	math	PROPN
ejpam-2985	42	6	,	,	PUNCT
ejpam-2985	42	7	10	10	NUM
ejpam-2985	42	8	(	(	PUNCT
ejpam-2985	42	9	3	3	NUM
ejpam-2985	42	10	)	)	PUNCT
ejpam-2985	42	11	(	(	PUNCT
ejpam-2985	42	12	2017	2017	NUM
ejpam-2985	42	13	)	)	PUNCT
ejpam-2985	42	14	,	,	PUNCT
ejpam-2985	42	15	473	473	NUM
ejpam-2985	42	16	-	-	SYM
ejpam-2985	42	17	487	487	NUM
ejpam-2985	42	18	475	475	NUM
ejpam-2985	42	19	definition	definition	NOUN
ejpam-2985	42	20	3	3	NUM
ejpam-2985	42	21	.	.	PUNCT
ejpam-2985	43	1	let	let	VERB
ejpam-2985	43	2	x	x	PRON
ejpam-2985	43	3	be	be	AUX
ejpam-2985	43	4	a	a	DET
ejpam-2985	43	5	nonempty	nonempty	ADJ
ejpam-2985	43	6	set	set	VERB
ejpam-2985	43	7	.	.	PUNCT
ejpam-2985	44	1	suppose	suppose	VERB
ejpam-2985	44	2	the	the	DET
ejpam-2985	44	3	mapping	mapping	NOUN
ejpam-2985	44	4	ρ	ρ	NOUN
ejpam-2985	44	5	:	:	PUNCT
ejpam-2985	44	6	x	x	X
ejpam-2985	44	7	×x	×x	X
ejpam-2985	44	8	→	→	SYM
ejpam-2985	44	9	e	e	NOUN
ejpam-2985	44	10	satisfies	satisfie	NOUN
ejpam-2985	44	11	:	:	PUNCT
ejpam-2985	44	12	(	(	PUNCT
ejpam-2985	44	13	i	i	NOUN
ejpam-2985	44	14	)	)	PUNCT
ejpam-2985	44	15	0	0	PUNCT
ejpam-2985	45	1	<	<	X
ejpam-2985	45	2	ρ(x	ρ(x	PROPN
ejpam-2985	45	3	,	,	PUNCT
ejpam-2985	45	4	y	y	NOUN
ejpam-2985	45	5	)	)	PUNCT
ejpam-2985	45	6	for	for	ADP
ejpam-2985	45	7	all	all	DET
ejpam-2985	45	8	x	x	NOUN
ejpam-2985	45	9	,	,	PUNCT
ejpam-2985	45	10	y	y	PROPN
ejpam-2985	45	11	∈	∈	PROPN
ejpam-2985	45	12	x	x	X
ejpam-2985	45	13	and	and	CCONJ
ejpam-2985	45	14	ρ(x	ρ(x	PROPN
ejpam-2985	45	15	,	,	PUNCT
ejpam-2985	45	16	y	y	NOUN
ejpam-2985	45	17	)	)	PUNCT
ejpam-2985	45	18	=	=	SYM
ejpam-2985	45	19	0	0	PUNCT
ejpam-2985	46	1	if	if	SCONJ
ejpam-2985	46	2	and	and	CCONJ
ejpam-2985	46	3	only	only	ADV
ejpam-2985	46	4	if	if	SCONJ
ejpam-2985	46	5	x	x	X
ejpam-2985	46	6	=	=	SYM
ejpam-2985	46	7	y	y	PROPN
ejpam-2985	46	8	;	;	PUNCT
ejpam-2985	46	9	(	(	PUNCT
ejpam-2985	46	10	ii	ii	NOUN
ejpam-2985	46	11	)	)	PUNCT
ejpam-2985	46	12	ρ(x	ρ(x	PROPN
ejpam-2985	46	13	,	,	PUNCT
ejpam-2985	46	14	y	y	NOUN
ejpam-2985	46	15	)	)	PUNCT
ejpam-2985	46	16	=	=	SYM
ejpam-2985	46	17	ρ(y	ρ(y	NOUN
ejpam-2985	46	18	,	,	PUNCT
ejpam-2985	46	19	x	x	NOUN
ejpam-2985	46	20	)	)	PUNCT
ejpam-2985	46	21	for	for	ADP
ejpam-2985	46	22	all	all	DET
ejpam-2985	46	23	x	x	NOUN
ejpam-2985	46	24	,	,	PUNCT
ejpam-2985	46	25	y	y	PROPN
ejpam-2985	46	26	∈	∈	PROPN
ejpam-2985	46	27	x	x	X
ejpam-2985	46	28	;	;	PUNCT
ejpam-2985	46	29	(	(	PUNCT
ejpam-2985	46	30	iii	iii	NOUN
ejpam-2985	46	31	)	)	PUNCT
ejpam-2985	46	32	ρ(x	ρ(x	PROPN
ejpam-2985	46	33	,	,	PUNCT
ejpam-2985	46	34	y	y	NOUN
ejpam-2985	46	35	)	)	PUNCT
ejpam-2985	46	36	≤	≤	NOUN
ejpam-2985	46	37	ρ(x	ρ(x	NOUN
ejpam-2985	46	38	,	,	PUNCT
ejpam-2985	46	39	w	w	NOUN
ejpam-2985	46	40	)	)	PUNCT
ejpam-2985	46	41	+	+	CCONJ
ejpam-2985	46	42	ρ(w	ρ(w	PROPN
ejpam-2985	46	43	,	,	PUNCT
ejpam-2985	46	44	z	z	NOUN
ejpam-2985	46	45	)	)	PUNCT
ejpam-2985	46	46	+	+	CCONJ
ejpam-2985	46	47	ρ(z	ρ(z	PROPN
ejpam-2985	46	48	,	,	PUNCT
ejpam-2985	46	49	y	y	NOUN
ejpam-2985	46	50	)	)	PUNCT
ejpam-2985	46	51	for	for	ADP
ejpam-2985	46	52	all	all	DET
ejpam-2985	46	53	x	x	NOUN
ejpam-2985	46	54	,	,	PUNCT
ejpam-2985	46	55	y	y	PROPN
ejpam-2985	46	56	,	,	PUNCT
ejpam-2985	46	57	z	z	NOUN
ejpam-2985	46	58	∈	∈	PROPN
ejpam-2985	46	59	x	x	X
ejpam-2985	46	60	and	and	CCONJ
ejpam-2985	46	61	for	for	ADP
ejpam-2985	46	62	all	all	DET
ejpam-2985	46	63	distinct	distinct	ADJ
ejpam-2985	46	64	points	point	NOUN
ejpam-2985	46	65	w	w	NOUN
ejpam-2985	46	66	,	,	PUNCT
ejpam-2985	46	67	z	z	NOUN
ejpam-2985	46	68	∈	∈	PROPN
ejpam-2985	46	69	x	x	PUNCT
ejpam-2985	46	70	−	−	PROPN
ejpam-2985	46	71	{	{	PUNCT
ejpam-2985	46	72	x	x	NOUN
ejpam-2985	46	73	,	,	PUNCT
ejpam-2985	46	74	y	y	PROPN
ejpam-2985	46	75	}	}	PUNCT
ejpam-2985	47	1	[	[	X
ejpam-2985	47	2	rectangular	rectangular	ADJ
ejpam-2985	47	3	property	property	NOUN
ejpam-2985	47	4	]	]	PUNCT
ejpam-2985	47	5	.	.	PUNCT
ejpam-2985	48	1	then	then	ADV
ejpam-2985	48	2	ρ	ρ	PROPN
ejpam-2985	48	3	is	be	AUX
ejpam-2985	48	4	called	call	VERB
ejpam-2985	48	5	a	a	DET
ejpam-2985	48	6	cone	cone	NOUN
ejpam-2985	48	7	rectangular	rectangular	ADJ
ejpam-2985	48	8	metric	metric	NOUN
ejpam-2985	48	9	on	on	ADP
ejpam-2985	48	10	x	x	PRON
ejpam-2985	48	11	,	,	PUNCT
ejpam-2985	48	12	and	and	CCONJ
ejpam-2985	48	13	(	(	PUNCT
ejpam-2985	48	14	x	x	X
ejpam-2985	48	15	,	,	PUNCT
ejpam-2985	48	16	ρ	ρ	PROPN
ejpam-2985	48	17	)	)	PUNCT
ejpam-2985	48	18	is	be	AUX
ejpam-2985	48	19	called	call	VERB
ejpam-2985	48	20	a	a	DET
ejpam-2985	48	21	cone	cone	NOUN
ejpam-2985	48	22	rectangular	rectangular	ADJ
ejpam-2985	48	23	metric	metric	ADJ
ejpam-2985	48	24	space	space	NOUN
ejpam-2985	48	25	.	.	PUNCT
ejpam-2985	49	1	remark	remark	PROPN
ejpam-2985	49	2	1	1	NUM
ejpam-2985	49	3	.	.	PUNCT
ejpam-2985	50	1	every	every	DET
ejpam-2985	50	2	cone	cone	NOUN
ejpam-2985	50	3	metric	metric	ADJ
ejpam-2985	50	4	space	space	NOUN
ejpam-2985	50	5	is	be	AUX
ejpam-2985	50	6	cone	cone	NOUN
ejpam-2985	50	7	rectangular	rectangular	ADJ
ejpam-2985	50	8	metric	metric	ADJ
ejpam-2985	50	9	space	space	NOUN
ejpam-2985	50	10	.	.	PUNCT
ejpam-2985	51	1	the	the	DET
ejpam-2985	51	2	converse	converse	NOUN
ejpam-2985	51	3	is	be	AUX
ejpam-2985	51	4	not	not	PART
ejpam-2985	51	5	necessarily	necessarily	ADV
ejpam-2985	51	6	true	true	ADJ
ejpam-2985	51	7	(	(	PUNCT
ejpam-2985	51	8	e.g.	e.g.	ADV
ejpam-2985	51	9	,	,	PUNCT
ejpam-2985	51	10	see	see	VERB
ejpam-2985	51	11	[	[	X
ejpam-2985	51	12	6	6	NUM
ejpam-2985	51	13	]	]	NUM
ejpam-2985	51	14	)	)	PUNCT
ejpam-2985	51	15	.	.	PUNCT
ejpam-2985	52	1	definition	definition	NOUN
ejpam-2985	52	2	4	4	X
ejpam-2985	52	3	.	.	PUNCT
ejpam-2985	53	1	let	let	VERB
ejpam-2985	53	2	x	x	PRON
ejpam-2985	53	3	be	be	AUX
ejpam-2985	53	4	a	a	DET
ejpam-2985	53	5	non	non	X
ejpam-2985	53	6	empty	empty	ADJ
ejpam-2985	53	7	set	set	NOUN
ejpam-2985	53	8	.	.	PUNCT
ejpam-2985	54	1	suppose	suppose	VERB
ejpam-2985	54	2	the	the	DET
ejpam-2985	54	3	mapping	mapping	NOUN
ejpam-2985	54	4	d	d	NOUN
ejpam-2985	54	5	:	:	PUNCT
ejpam-2985	54	6	x	x	PROPN
ejpam-2985	54	7	×x	×x	X
ejpam-2985	54	8	→	→	SYM
ejpam-2985	54	9	e	e	NOUN
ejpam-2985	54	10	satisfies	satisfie	NOUN
ejpam-2985	54	11	:	:	PUNCT
ejpam-2985	54	12	(	(	PUNCT
ejpam-2985	54	13	i	i	NOUN
ejpam-2985	54	14	)	)	PUNCT
ejpam-2985	54	15	0	0	PUNCT
ejpam-2985	55	1	<	<	X
ejpam-2985	55	2	d(x	d(x	PROPN
ejpam-2985	55	3	,	,	PUNCT
ejpam-2985	55	4	y	y	NOUN
ejpam-2985	55	5	)	)	PUNCT
ejpam-2985	55	6	for	for	ADP
ejpam-2985	55	7	all	all	DET
ejpam-2985	55	8	x	x	NOUN
ejpam-2985	55	9	,	,	PUNCT
ejpam-2985	55	10	y	y	PROPN
ejpam-2985	55	11	∈	∈	PROPN
ejpam-2985	55	12	x	x	X
ejpam-2985	55	13	and	and	CCONJ
ejpam-2985	55	14	d(x	d(x	PROPN
ejpam-2985	55	15	,	,	PUNCT
ejpam-2985	55	16	y	y	NOUN
ejpam-2985	55	17	)	)	PUNCT
ejpam-2985	55	18	=	=	SYM
ejpam-2985	55	19	0	0	PUNCT
ejpam-2985	56	1	if	if	SCONJ
ejpam-2985	56	2	and	and	CCONJ
ejpam-2985	56	3	only	only	ADV
ejpam-2985	56	4	if	if	SCONJ
ejpam-2985	56	5	x	x	X
ejpam-2985	56	6	=	=	SYM
ejpam-2985	56	7	y	y	PROPN
ejpam-2985	56	8	;	;	PUNCT
ejpam-2985	56	9	(	(	PUNCT
ejpam-2985	56	10	ii	ii	NOUN
ejpam-2985	56	11	)	)	PUNCT
ejpam-2985	56	12	d(x	d(x	PROPN
ejpam-2985	56	13	,	,	PUNCT
ejpam-2985	56	14	y	y	NOUN
ejpam-2985	56	15	)	)	PUNCT
ejpam-2985	56	16	=	=	SYM
ejpam-2985	56	17	d(y	d(y	NOUN
ejpam-2985	56	18	,	,	PUNCT
ejpam-2985	56	19	x	x	NOUN
ejpam-2985	56	20	)	)	PUNCT
ejpam-2985	56	21	for	for	ADP
ejpam-2985	56	22	x	x	X
ejpam-2985	56	23	,	,	PUNCT
ejpam-2985	56	24	y	y	PROPN
ejpam-2985	56	25	∈	∈	PROPN
ejpam-2985	56	26	x	x	X
ejpam-2985	56	27	;	;	PUNCT
ejpam-2985	56	28	(	(	PUNCT
ejpam-2985	56	29	iii	iii	NOUN
ejpam-2985	56	30	)	)	PUNCT
ejpam-2985	56	31	d(x	d(x	PROPN
ejpam-2985	56	32	,	,	PUNCT
ejpam-2985	56	33	y	y	NOUN
ejpam-2985	56	34	)	)	PUNCT
ejpam-2985	56	35	≤	≤	NOUN
ejpam-2985	56	36	d(x	d(x	NOUN
ejpam-2985	56	37	,	,	PUNCT
ejpam-2985	56	38	z	z	NOUN
ejpam-2985	56	39	)	)	PUNCT
ejpam-2985	57	1	+	+	CCONJ
ejpam-2985	57	2	d(z	d(z	PROPN
ejpam-2985	57	3	,	,	PUNCT
ejpam-2985	57	4	w	w	NOUN
ejpam-2985	57	5	)	)	PUNCT
ejpam-2985	57	6	+	+	CCONJ
ejpam-2985	57	7	d(w	d(w	PROPN
ejpam-2985	57	8	,	,	PUNCT
ejpam-2985	57	9	u	u	NOUN
ejpam-2985	57	10	)	)	PUNCT
ejpam-2985	57	11	+	+	CCONJ
ejpam-2985	57	12	d(u	d(u	PROPN
ejpam-2985	57	13	,	,	PUNCT
ejpam-2985	57	14	y	y	NOUN
ejpam-2985	57	15	)	)	PUNCT
ejpam-2985	57	16	for	for	ADP
ejpam-2985	57	17	all	all	DET
ejpam-2985	57	18	x	x	NOUN
ejpam-2985	57	19	,	,	PUNCT
ejpam-2985	57	20	y	y	PROPN
ejpam-2985	57	21	,	,	PUNCT
ejpam-2985	57	22	z	z	PROPN
ejpam-2985	57	23	,	,	PUNCT
ejpam-2985	57	24	w	w	PROPN
ejpam-2985	57	25	,	,	PUNCT
ejpam-2985	57	26	u	u	NOUN
ejpam-2985	57	27	∈	∈	PROPN
ejpam-2985	57	28	x	x	X
ejpam-2985	57	29	and	and	CCONJ
ejpam-2985	57	30	for	for	ADP
ejpam-2985	57	31	all	all	DET
ejpam-2985	57	32	distinct	distinct	ADJ
ejpam-2985	57	33	points	point	NOUN
ejpam-2985	57	34	z	z	PROPN
ejpam-2985	57	35	,	,	PUNCT
ejpam-2985	57	36	w	w	PROPN
ejpam-2985	57	37	,	,	PUNCT
ejpam-2985	57	38	u,∈	u,∈	PROPN
ejpam-2985	57	39	x	x	SYM
ejpam-2985	57	40	−	−	X
ejpam-2985	57	41	{	{	PUNCT
ejpam-2985	57	42	x	x	NOUN
ejpam-2985	57	43	,	,	PUNCT
ejpam-2985	57	44	y	y	PROPN
ejpam-2985	57	45	}	}	PUNCT
ejpam-2985	58	1	[	[	X
ejpam-2985	58	2	pentagonal	pentagonal	ADJ
ejpam-2985	58	3	property	property	NOUN
ejpam-2985	58	4	]	]	PUNCT
ejpam-2985	58	5	.	.	PUNCT
ejpam-2985	59	1	then	then	ADV
ejpam-2985	59	2	d	d	PROPN
ejpam-2985	59	3	is	be	AUX
ejpam-2985	59	4	called	call	VERB
ejpam-2985	59	5	a	a	DET
ejpam-2985	59	6	cone	cone	NOUN
ejpam-2985	59	7	pentagonal	pentagonal	ADJ
ejpam-2985	59	8	metric	metric	NOUN
ejpam-2985	59	9	on	on	ADP
ejpam-2985	59	10	x	x	PRON
ejpam-2985	59	11	,	,	PUNCT
ejpam-2985	59	12	and	and	CCONJ
ejpam-2985	59	13	(	(	PUNCT
ejpam-2985	59	14	x	x	X
ejpam-2985	59	15	,	,	PUNCT
ejpam-2985	59	16	d	d	NOUN
ejpam-2985	59	17	)	)	PUNCT
ejpam-2985	59	18	is	be	AUX
ejpam-2985	59	19	called	call	VERB
ejpam-2985	59	20	a	a	DET
ejpam-2985	59	21	cone	cone	NOUN
ejpam-2985	59	22	pentagonal	pentagonal	ADJ
ejpam-2985	59	23	metric	metric	ADJ
ejpam-2985	59	24	space	space	NOUN
ejpam-2985	59	25	.	.	PUNCT
ejpam-2985	60	1	remark	remark	NOUN
ejpam-2985	60	2	2	2	NUM
ejpam-2985	60	3	.	.	PUNCT
ejpam-2985	61	1	every	every	DET
ejpam-2985	61	2	cone	cone	NOUN
ejpam-2985	61	3	rectangular	rectangular	ADJ
ejpam-2985	61	4	metric	metric	ADJ
ejpam-2985	61	5	space	space	NOUN
ejpam-2985	61	6	and	and	CCONJ
ejpam-2985	61	7	so	so	ADV
ejpam-2985	61	8	cone	cone	NOUN
ejpam-2985	61	9	metric	metric	ADJ
ejpam-2985	61	10	space	space	NOUN
ejpam-2985	61	11	is	be	AUX
ejpam-2985	61	12	cone	cone	NOUN
ejpam-2985	61	13	pentagonal	pentagonal	ADJ
ejpam-2985	61	14	metric	metric	ADJ
ejpam-2985	61	15	space	space	NOUN
ejpam-2985	61	16	.	.	PUNCT
ejpam-2985	62	1	the	the	DET
ejpam-2985	62	2	converse	converse	NOUN
ejpam-2985	62	3	is	be	AUX
ejpam-2985	62	4	not	not	PART
ejpam-2985	62	5	necessarily	necessarily	ADV
ejpam-2985	62	6	true	true	ADJ
ejpam-2985	62	7	(	(	PUNCT
ejpam-2985	62	8	e.g.	e.g.	ADV
ejpam-2985	62	9	,	,	PUNCT
ejpam-2985	62	10	see	see	VERB
ejpam-2985	62	11	[	[	X
ejpam-2985	62	12	9	9	NUM
ejpam-2985	62	13	]	]	PUNCT
ejpam-2985	62	14	)	)	PUNCT
ejpam-2985	62	15	.	.	PUNCT
ejpam-2985	63	1	let	let	VERB
ejpam-2985	63	2	(	(	PUNCT
ejpam-2985	63	3	x	x	NOUN
ejpam-2985	63	4	,	,	PUNCT
ejpam-2985	63	5	d	d	NOUN
ejpam-2985	63	6	)	)	PUNCT
ejpam-2985	63	7	be	be	AUX
ejpam-2985	63	8	a	a	DET
ejpam-2985	63	9	cone	cone	NOUN
ejpam-2985	63	10	pentagonal	pentagonal	ADJ
ejpam-2985	63	11	metric	metric	ADJ
ejpam-2985	63	12	space	space	NOUN
ejpam-2985	63	13	.	.	PUNCT
ejpam-2985	64	1	let	let	VERB
ejpam-2985	64	2	{	{	PUNCT
ejpam-2985	64	3	xn	xn	VERB
ejpam-2985	64	4	}	}	PUNCT
ejpam-2985	64	5	be	be	AUX
ejpam-2985	64	6	a	a	DET
ejpam-2985	64	7	sequence	sequence	NOUN
ejpam-2985	64	8	in	in	ADP
ejpam-2985	64	9	x	x	PUNCT
ejpam-2985	64	10	and	and	CCONJ
ejpam-2985	64	11	x	x	SYM
ejpam-2985	64	12	∈	∈	PROPN
ejpam-2985	64	13	x.	x.	NOUN
ejpam-2985	65	1	if	if	SCONJ
ejpam-2985	65	2	for	for	ADP
ejpam-2985	65	3	every	every	DET
ejpam-2985	65	4	c	c	NOUN
ejpam-2985	65	5	∈	∈	PROPN
ejpam-2985	65	6	e	e	X
ejpam-2985	65	7	with	with	ADP
ejpam-2985	65	8	0	0	NUM
ejpam-2985	65	9	�	�	PROPN
ejpam-2985	65	10	c	c	NOUN
ejpam-2985	65	11	there	there	PRON
ejpam-2985	65	12	exist	exist	VERB
ejpam-2985	65	13	n0	n0	X
ejpam-2985	65	14	∈	∈	PROPN
ejpam-2985	65	15	n	n	PRON
ejpam-2985	65	16	and	and	CCONJ
ejpam-2985	65	17	that	that	SCONJ
ejpam-2985	65	18	for	for	ADP
ejpam-2985	65	19	all	all	DET
ejpam-2985	65	20	n	n	PROPN
ejpam-2985	65	21	>	>	X
ejpam-2985	65	22	n0	n0	PROPN
ejpam-2985	65	23	,	,	PUNCT
ejpam-2985	65	24	d(xn	d(xn	PROPN
ejpam-2985	66	1	,	,	PUNCT
ejpam-2985	66	2	x	x	X
ejpam-2985	66	3	)	)	PUNCT
ejpam-2985	66	4	�	�	PROPN
ejpam-2985	66	5	c	c	NOUN
ejpam-2985	66	6	,	,	PUNCT
ejpam-2985	66	7	then	then	ADV
ejpam-2985	66	8	{	{	PUNCT
ejpam-2985	66	9	xn	xn	X
ejpam-2985	66	10	}	}	PUNCT
ejpam-2985	66	11	is	be	AUX
ejpam-2985	66	12	said	say	VERB
ejpam-2985	66	13	to	to	PART
ejpam-2985	66	14	be	be	AUX
ejpam-2985	66	15	convergent	convergent	ADJ
ejpam-2985	66	16	and	and	CCONJ
ejpam-2985	66	17	{	{	PUNCT
ejpam-2985	66	18	xn	xn	NOUN
ejpam-2985	66	19	}	}	PUNCT
ejpam-2985	66	20	converges	converge	NOUN
ejpam-2985	66	21	to	to	ADP
ejpam-2985	66	22	x	x	PRON
ejpam-2985	66	23	,	,	PUNCT
ejpam-2985	66	24	and	and	CCONJ
ejpam-2985	66	25	x	x	X
ejpam-2985	66	26	is	be	AUX
ejpam-2985	66	27	the	the	DET
ejpam-2985	66	28	limit	limit	NOUN
ejpam-2985	66	29	of	of	ADP
ejpam-2985	66	30	{	{	PUNCT
ejpam-2985	66	31	xn	xn	NUM
ejpam-2985	66	32	}	}	PUNCT
ejpam-2985	66	33	.	.	PUNCT
ejpam-2985	67	1	we	we	PRON
ejpam-2985	67	2	denote	denote	VERB
ejpam-2985	67	3	this	this	PRON
ejpam-2985	67	4	by	by	ADP
ejpam-2985	67	5	limn→∞	limn→∞	PROPN
ejpam-2985	67	6	xn	xn	PUNCT
ejpam-2985	68	1	=	=	SYM
ejpam-2985	68	2	x	x	PROPN
ejpam-2985	68	3	or	or	CCONJ
ejpam-2985	68	4	xn	xn	PROPN
ejpam-2985	68	5	→	→	SYM
ejpam-2985	68	6	x	x	X
ejpam-2985	68	7	as	as	ADP
ejpam-2985	68	8	n	n	NOUN
ejpam-2985	68	9	→	→	SYM
ejpam-2985	68	10	∞.	∞.	PROPN
ejpam-2985	68	11	if	if	SCONJ
ejpam-2985	68	12	for	for	ADP
ejpam-2985	68	13	every	every	DET
ejpam-2985	68	14	c	c	PROPN
ejpam-2985	68	15	∈	∈	PROPN
ejpam-2985	68	16	e	e	NOUN
ejpam-2985	68	17	,	,	PUNCT
ejpam-2985	68	18	with	with	ADP
ejpam-2985	68	19	0	0	NUM
ejpam-2985	68	20	�	�	PROPN
ejpam-2985	68	21	c	c	NOUN
ejpam-2985	68	22	there	there	PRON
ejpam-2985	68	23	exist	exist	VERB
ejpam-2985	68	24	n0	n0	X
ejpam-2985	68	25	∈	∈	PROPN
ejpam-2985	68	26	n	n	PRON
ejpam-2985	68	27	such	such	ADJ
ejpam-2985	68	28	that	that	PRON
ejpam-2985	68	29	for	for	ADP
ejpam-2985	68	30	all	all	DET
ejpam-2985	68	31	n	n	CCONJ
ejpam-2985	68	32	,	,	PUNCT
ejpam-2985	68	33	m	m	VERB
ejpam-2985	68	34	>	>	X
ejpam-2985	68	35	n0	n0	PROPN
ejpam-2985	68	36	,	,	PUNCT
ejpam-2985	68	37	d(xn	d(xn	PROPN
ejpam-2985	69	1	,	,	PUNCT
ejpam-2985	69	2	xm	xm	PROPN
ejpam-2985	69	3	)	)	PUNCT
ejpam-2985	69	4	�	�	PROPN
ejpam-2985	69	5	c	c	PROPN
ejpam-2985	69	6	,	,	PUNCT
ejpam-2985	69	7	then	then	ADV
ejpam-2985	69	8	{	{	PUNCT
ejpam-2985	69	9	xn	xn	X
ejpam-2985	69	10	}	}	PUNCT
ejpam-2985	69	11	is	be	AUX
ejpam-2985	69	12	called	call	VERB
ejpam-2985	69	13	cauchy	cauchy	ADJ
ejpam-2985	69	14	sequence	sequence	NOUN
ejpam-2985	69	15	in	in	ADP
ejpam-2985	69	16	x.	x.	NOUN
ejpam-2985	69	17	if	if	SCONJ
ejpam-2985	69	18	every	every	DET
ejpam-2985	69	19	cauchy	cauchy	ADJ
ejpam-2985	69	20	sequence	sequence	NOUN
ejpam-2985	69	21	is	be	AUX
ejpam-2985	69	22	convergent	convergent	ADJ
ejpam-2985	69	23	in	in	ADP
ejpam-2985	69	24	x	x	NOUN
ejpam-2985	69	25	,	,	PUNCT
ejpam-2985	69	26	then	then	ADV
ejpam-2985	69	27	x	x	PUNCT
ejpam-2985	69	28	is	be	AUX
ejpam-2985	69	29	called	call	VERB
ejpam-2985	69	30	a	a	DET
ejpam-2985	69	31	complete	complete	ADJ
ejpam-2985	69	32	cone	cone	NOUN
ejpam-2985	69	33	pentagonal	pentagonal	ADJ
ejpam-2985	69	34	metric	metric	ADJ
ejpam-2985	69	35	space	space	NOUN
ejpam-2985	69	36	.	.	PUNCT
ejpam-2985	70	1	definition	definition	NOUN
ejpam-2985	70	2	5	5	NUM
ejpam-2985	70	3	.	.	PUNCT
ejpam-2985	71	1	let	let	VERB
ejpam-2985	71	2	p	p	PRON
ejpam-2985	71	3	be	be	AUX
ejpam-2985	71	4	a	a	DET
ejpam-2985	71	5	cone	cone	NOUN
ejpam-2985	71	6	defined	define	VERB
ejpam-2985	71	7	as	as	ADP
ejpam-2985	71	8	above	above	ADV
ejpam-2985	71	9	and	and	CCONJ
ejpam-2985	71	10	let	let	VERB
ejpam-2985	71	11	φ	φ	PROPN
ejpam-2985	71	12	be	be	AUX
ejpam-2985	71	13	the	the	DET
ejpam-2985	71	14	set	set	NOUN
ejpam-2985	71	15	of	of	ADP
ejpam-2985	71	16	non	non	ADJ
ejpam-2985	71	17	decreasing	decrease	VERB
ejpam-2985	71	18	continuous	continuous	ADJ
ejpam-2985	71	19	functions	function	NOUN
ejpam-2985	71	20	ϕ	ϕ	NOUN
ejpam-2985	71	21	:	:	PUNCT
ejpam-2985	71	22	p	p	X
ejpam-2985	71	23	→	→	X
ejpam-2985	71	24	p	p	X
ejpam-2985	71	25	satisfying	satisfying	NOUN
ejpam-2985	71	26	:	:	PUNCT
ejpam-2985	71	27	(	(	PUNCT
ejpam-2985	71	28	i	i	NOUN
ejpam-2985	71	29	)	)	PUNCT
ejpam-2985	71	30	0	0	PUNCT
ejpam-2985	72	1	<	<	X
ejpam-2985	72	2	ϕ(t	ϕ(t	NUM
ejpam-2985	72	3	)	)	PUNCT
ejpam-2985	72	4	<	<	X
ejpam-2985	72	5	t	t	PROPN
ejpam-2985	72	6	for	for	ADP
ejpam-2985	72	7	all	all	DET
ejpam-2985	72	8	t	t	NOUN
ejpam-2985	72	9	∈	∈	PROPN
ejpam-2985	72	10	p	p	X
ejpam-2985	72	11	\	\	PROPN
ejpam-2985	72	12	{	{	PUNCT
ejpam-2985	72	13	0	0	NUM
ejpam-2985	72	14	}	}	PUNCT
ejpam-2985	72	15	,	,	PUNCT
ejpam-2985	72	16	(	(	PUNCT
ejpam-2985	72	17	ii	ii	NOUN
ejpam-2985	72	18	)	)	PUNCT
ejpam-2985	72	19	the	the	DET
ejpam-2985	72	20	series	series	NOUN
ejpam-2985	72	21	∑	∑	PROPN
ejpam-2985	72	22	n≥0	n≥0	PROPN
ejpam-2985	72	23	ϕ	ϕ	PROPN
ejpam-2985	72	24	n(t	n(t	PROPN
ejpam-2985	72	25	)	)	PUNCT
ejpam-2985	72	26	converge	converge	VERB
ejpam-2985	72	27	for	for	ADP
ejpam-2985	72	28	all	all	DET
ejpam-2985	72	29	t	t	NOUN
ejpam-2985	72	30	∈	∈	PROPN
ejpam-2985	72	31	p	p	X
ejpam-2985	72	32	\	\	PROPN
ejpam-2985	72	33	{	{	PUNCT
ejpam-2985	72	34	0	0	NUM
ejpam-2985	72	35	}	}	PUNCT
ejpam-2985	72	36	from	from	ADP
ejpam-2985	72	37	(	(	PUNCT
ejpam-2985	72	38	i	i	NOUN
ejpam-2985	72	39	)	)	PUNCT
ejpam-2985	72	40	,	,	PUNCT
ejpam-2985	72	41	we	we	PRON
ejpam-2985	72	42	have	have	VERB
ejpam-2985	72	43	ϕ(0	ϕ(0	PRON
ejpam-2985	72	44	)	)	PUNCT
ejpam-2985	73	1	=	=	PUNCT
ejpam-2985	73	2	0	0	NUM
ejpam-2985	73	3	,	,	PUNCT
ejpam-2985	73	4	and	and	CCONJ
ejpam-2985	73	5	from	from	ADP
ejpam-2985	73	6	(	(	PUNCT
ejpam-2985	73	7	ii	ii	NOUN
ejpam-2985	73	8	)	)	PUNCT
ejpam-2985	73	9	,	,	PUNCT
ejpam-2985	73	10	we	we	PRON
ejpam-2985	73	11	have	have	VERB
ejpam-2985	73	12	limn→0	limn→0	PROPN
ejpam-2985	73	13	ϕ	ϕ	PROPN
ejpam-2985	73	14	n(t	n(t	PROPN
ejpam-2985	73	15	)	)	PUNCT
ejpam-2985	74	1	=	=	SYM
ejpam-2985	74	2	0	0	NUM
ejpam-2985	75	1	for	for	ADP
ejpam-2985	75	2	all	all	DET
ejpam-2985	75	3	t	t	NOUN
ejpam-2985	75	4	∈	∈	PROPN
ejpam-2985	75	5	p	p	X
ejpam-2985	75	6	\	\	PROPN
ejpam-2985	75	7	{	{	PUNCT
ejpam-2985	75	8	0	0	NUM
ejpam-2985	75	9	}	}	PUNCT
ejpam-2985	75	10	.	.	PUNCT
ejpam-2985	76	1	let	let	VERB
ejpam-2985	76	2	t	t	NOUN
ejpam-2985	76	3	and	and	CCONJ
ejpam-2985	76	4	s	s	AUX
ejpam-2985	76	5	be	be	AUX
ejpam-2985	76	6	self	self	NOUN
ejpam-2985	76	7	maps	map	NOUN
ejpam-2985	76	8	of	of	ADP
ejpam-2985	76	9	a	a	DET
ejpam-2985	76	10	nonempty	nonempty	ADV
ejpam-2985	76	11	set	set	VERB
ejpam-2985	76	12	x.	x.	NOUN
ejpam-2985	77	1	if	if	SCONJ
ejpam-2985	77	2	w	w	PROPN
ejpam-2985	77	3	=	=	VERB
ejpam-2985	77	4	tx	tx	PROPN
ejpam-2985	77	5	=	=	PUNCT
ejpam-2985	77	6	sx	sx	PROPN
ejpam-2985	77	7	for	for	ADP
ejpam-2985	77	8	some	some	DET
ejpam-2985	77	9	x	x	SYM
ejpam-2985	77	10	∈	∈	PROPN
ejpam-2985	77	11	x	x	NOUN
ejpam-2985	77	12	,	,	PUNCT
ejpam-2985	77	13	then	then	ADV
ejpam-2985	77	14	x	x	PUNCT
ejpam-2985	77	15	is	be	AUX
ejpam-2985	77	16	called	call	VERB
ejpam-2985	77	17	a	a	DET
ejpam-2985	77	18	coincidence	coincidence	NOUN
ejpam-2985	77	19	point	point	NOUN
ejpam-2985	77	20	of	of	ADP
ejpam-2985	77	21	t	t	PROPN
ejpam-2985	77	22	and	and	CCONJ
ejpam-2985	77	23	s	s	PROPN
ejpam-2985	77	24	and	and	CCONJ
ejpam-2985	77	25	w	w	PROPN
ejpam-2985	77	26	is	be	AUX
ejpam-2985	77	27	called	call	VERB
ejpam-2985	77	28	a	a	DET
ejpam-2985	77	29	point	point	NOUN
ejpam-2985	77	30	of	of	ADP
ejpam-2985	77	31	coincidence	coincidence	NOUN
ejpam-2985	77	32	of	of	ADP
ejpam-2985	77	33	t	t	PROPN
ejpam-2985	77	34	and	and	CCONJ
ejpam-2985	77	35	s.	s.	PROPN
ejpam-2985	77	36	also	also	ADV
ejpam-2985	77	37	,	,	PUNCT
ejpam-2985	77	38	t	t	PROPN
ejpam-2985	77	39	and	and	CCONJ
ejpam-2985	77	40	s	s	PRON
ejpam-2985	77	41	are	be	AUX
ejpam-2985	77	42	said	say	VERB
ejpam-2985	77	43	to	to	PART
ejpam-2985	77	44	be	be	AUX
ejpam-2985	77	45	weakly	weakly	ADV
ejpam-2985	77	46	compatible	compatible	ADJ
ejpam-2985	77	47	if	if	SCONJ
ejpam-2985	77	48	they	they	PRON
ejpam-2985	77	49	commute	commute	VERB
ejpam-2985	77	50	at	at	ADP
ejpam-2985	77	51	their	their	PRON
ejpam-2985	77	52	coincidence	coincidence	NOUN
ejpam-2985	77	53	points	point	NOUN
ejpam-2985	77	54	,	,	PUNCT
ejpam-2985	77	55	that	that	ADV
ejpam-2985	77	56	is	is	ADV
ejpam-2985	77	57	,	,	PUNCT
ejpam-2985	77	58	tx	tx	PROPN
ejpam-2985	77	59	=	=	PUNCT
ejpam-2985	77	60	sx	sx	PROPN
ejpam-2985	77	61	implies	imply	VERB
ejpam-2985	77	62	that	that	SCONJ
ejpam-2985	77	63	tsx	tsx	PROPN
ejpam-2985	77	64	=	=	PROPN
ejpam-2985	77	65	stx	stx	PROPN
ejpam-2985	77	66	.	.	PUNCT
ejpam-2985	77	67	a.	a.	PROPN
ejpam-2985	77	68	auwalu	auwalu	PROPN
ejpam-2985	77	69	,	,	PUNCT
ejpam-2985	77	70	e.	e.	PROPN
ejpam-2985	77	71	hınçal	hınçal	PROPN
ejpam-2985	77	72	/	/	SYM
ejpam-2985	77	73	eur	eur	PROPN
ejpam-2985	77	74	.	.	PUNCT
ejpam-2985	78	1	j.	j.	PROPN
ejpam-2985	78	2	pure	pure	PROPN
ejpam-2985	78	3	appl	appl	PROPN
ejpam-2985	78	4	.	.	PROPN
ejpam-2985	78	5	math	math	PROPN
ejpam-2985	78	6	,	,	PUNCT
ejpam-2985	78	7	10	10	NUM
ejpam-2985	78	8	(	(	PUNCT
ejpam-2985	78	9	3	3	NUM
ejpam-2985	78	10	)	)	PUNCT
ejpam-2985	78	11	(	(	PUNCT
ejpam-2985	78	12	2017	2017	NUM
ejpam-2985	78	13	)	)	PUNCT
ejpam-2985	78	14	,	,	PUNCT
ejpam-2985	78	15	473	473	NUM
ejpam-2985	78	16	-	-	SYM
ejpam-2985	78	17	487	487	NUM
ejpam-2985	78	18	476	476	NUM
ejpam-2985	78	19	lemma	lemma	PROPN
ejpam-2985	78	20	1	1	X
ejpam-2985	78	21	.	.	PUNCT
ejpam-2985	79	1	let	let	VERB
ejpam-2985	79	2	t	t	PROPN
ejpam-2985	79	3	and	and	CCONJ
ejpam-2985	79	4	s	s	AUX
ejpam-2985	79	5	be	be	AUX
ejpam-2985	79	6	weakly	weakly	ADV
ejpam-2985	79	7	compatible	compatible	ADJ
ejpam-2985	79	8	self	self	NOUN
ejpam-2985	79	9	mappings	mapping	NOUN
ejpam-2985	79	10	of	of	ADP
ejpam-2985	79	11	nonempty	nonempty	ADV
ejpam-2985	79	12	set	set	VERB
ejpam-2985	79	13	x.	x.	NOUN
ejpam-2985	80	1	if	if	SCONJ
ejpam-2985	80	2	t	t	PROPN
ejpam-2985	80	3	and	and	CCONJ
ejpam-2985	80	4	s	s	AUX
ejpam-2985	80	5	have	have	VERB
ejpam-2985	80	6	a	a	DET
ejpam-2985	80	7	unique	unique	ADJ
ejpam-2985	80	8	point	point	NOUN
ejpam-2985	80	9	of	of	ADP
ejpam-2985	80	10	coincidence	coincidence	NOUN
ejpam-2985	80	11	w	w	PROPN
ejpam-2985	80	12	=	=	PUNCT
ejpam-2985	80	13	tx	tx	PROPN
ejpam-2985	80	14	=	=	SYM
ejpam-2985	80	15	sx	sx	PROPN
ejpam-2985	80	16	,	,	PUNCT
ejpam-2985	80	17	then	then	ADV
ejpam-2985	80	18	w	w	PROPN
ejpam-2985	80	19	is	be	AUX
ejpam-2985	80	20	the	the	DET
ejpam-2985	80	21	unique	unique	ADJ
ejpam-2985	80	22	common	common	ADJ
ejpam-2985	80	23	fixed	fix	VERB
ejpam-2985	80	24	point	point	NOUN
ejpam-2985	80	25	of	of	ADP
ejpam-2985	80	26	t	t	PROPN
ejpam-2985	80	27	and	and	CCONJ
ejpam-2985	80	28	s.	s.	PROPN
ejpam-2985	80	29	lemma	lemma	PROPN
ejpam-2985	81	1	2	2	X
ejpam-2985	81	2	.	.	PUNCT
ejpam-2985	81	3	let	let	VERB
ejpam-2985	81	4	(	(	PUNCT
ejpam-2985	81	5	x	x	NOUN
ejpam-2985	81	6	,	,	PUNCT
ejpam-2985	81	7	d	d	NOUN
ejpam-2985	81	8	)	)	PUNCT
ejpam-2985	81	9	be	be	AUX
ejpam-2985	81	10	a	a	DET
ejpam-2985	81	11	cone	cone	NOUN
ejpam-2985	81	12	metric	metric	ADJ
ejpam-2985	81	13	space	space	NOUN
ejpam-2985	81	14	with	with	ADP
ejpam-2985	81	15	cone	cone	NOUN
ejpam-2985	81	16	p	p	NOUN
ejpam-2985	81	17	not	not	PART
ejpam-2985	81	18	necessary	necessary	ADJ
ejpam-2985	81	19	to	to	PART
ejpam-2985	81	20	be	be	AUX
ejpam-2985	81	21	normal	normal	ADJ
ejpam-2985	81	22	.	.	PUNCT
ejpam-2985	82	1	then	then	ADV
ejpam-2985	82	2	for	for	ADP
ejpam-2985	82	3	a	a	DET
ejpam-2985	82	4	,	,	PUNCT
ejpam-2985	82	5	c	c	NOUN
ejpam-2985	82	6	,	,	PUNCT
ejpam-2985	82	7	u	u	NOUN
ejpam-2985	82	8	,	,	PUNCT
ejpam-2985	82	9	v	v	NOUN
ejpam-2985	82	10	,	,	PUNCT
ejpam-2985	82	11	w	w	PROPN
ejpam-2985	82	12	∈	∈	PROPN
ejpam-2985	82	13	e	e	NOUN
ejpam-2985	82	14	,	,	PUNCT
ejpam-2985	82	15	we	we	PRON
ejpam-2985	82	16	have	have	VERB
ejpam-2985	82	17	(	(	PUNCT
ejpam-2985	82	18	i	i	NOUN
ejpam-2985	82	19	)	)	PUNCT
ejpam-2985	82	20	if	if	SCONJ
ejpam-2985	82	21	a	a	DET
ejpam-2985	82	22	≤	≤	X
ejpam-2985	82	23	ha	ha	INTJ
ejpam-2985	82	24	and	and	CCONJ
ejpam-2985	82	25	h	h	NOUN
ejpam-2985	82	26	∈	∈	PROPN
ejpam-2985	83	1	[	[	X
ejpam-2985	83	2	0	0	NUM
ejpam-2985	83	3	,	,	PUNCT
ejpam-2985	83	4	1	1	NUM
ejpam-2985	83	5	)	)	PUNCT
ejpam-2985	83	6	,	,	PUNCT
ejpam-2985	83	7	then	then	ADV
ejpam-2985	83	8	a	a	DET
ejpam-2985	83	9	=	=	NOUN
ejpam-2985	83	10	0	0	NUM
ejpam-2985	83	11	.	.	PUNCT
ejpam-2985	83	12	(	(	PUNCT
ejpam-2985	83	13	ii	ii	NOUN
ejpam-2985	83	14	)	)	PUNCT
ejpam-2985	83	15	if	if	SCONJ
ejpam-2985	83	16	0	0	NUM
ejpam-2985	83	17	≤	≤	NUM
ejpam-2985	83	18	u	u	VERB
ejpam-2985	83	19	�	�	PROPN
ejpam-2985	83	20	c	c	PROPN
ejpam-2985	83	21	for	for	ADP
ejpam-2985	83	22	each	each	DET
ejpam-2985	83	23	0	0	NUM
ejpam-2985	83	24	�	�	PROPN
ejpam-2985	83	25	c	c	NOUN
ejpam-2985	83	26	,	,	PUNCT
ejpam-2985	83	27	then	then	ADV
ejpam-2985	83	28	u	u	X
ejpam-2985	83	29	=	=	PROPN
ejpam-2985	83	30	0	0	PROPN
ejpam-2985	83	31	.	.	PUNCT
ejpam-2985	83	32	(	(	PUNCT
ejpam-2985	83	33	iii	iii	X
ejpam-2985	83	34	)	)	PUNCT
ejpam-2985	83	35	if	if	SCONJ
ejpam-2985	83	36	u	u	NOUN
ejpam-2985	83	37	≤	≤	X
ejpam-2985	83	38	v	v	NOUN
ejpam-2985	83	39	and	and	CCONJ
ejpam-2985	83	40	v	v	ADP
ejpam-2985	83	41	�	�	PROPN
ejpam-2985	83	42	w	w	PROPN
ejpam-2985	83	43	,	,	PUNCT
ejpam-2985	83	44	then	then	ADV
ejpam-2985	83	45	u	u	PROPN
ejpam-2985	83	46	�	�	PROPN
ejpam-2985	83	47	w.	w.	PROPN
ejpam-2985	83	48	lemma	lemma	PROPN
ejpam-2985	83	49	3	3	X
ejpam-2985	83	50	.	.	PUNCT
ejpam-2985	84	1	let	let	AUX
ejpam-2985	84	2	(	(	PUNCT
ejpam-2985	84	3	x	x	NOUN
ejpam-2985	84	4	,	,	PUNCT
ejpam-2985	84	5	d	d	NOUN
ejpam-2985	84	6	)	)	PUNCT
ejpam-2985	84	7	be	be	AUX
ejpam-2985	84	8	a	a	DET
ejpam-2985	84	9	complete	complete	ADJ
ejpam-2985	84	10	cone	cone	NOUN
ejpam-2985	84	11	pentagonal	pentagonal	ADJ
ejpam-2985	84	12	metric	metric	ADJ
ejpam-2985	84	13	space	space	NOUN
ejpam-2985	84	14	.	.	PUNCT
ejpam-2985	85	1	let	let	VERB
ejpam-2985	85	2	{	{	PUNCT
ejpam-2985	85	3	xn	xn	VERB
ejpam-2985	85	4	}	}	PUNCT
ejpam-2985	85	5	be	be	AUX
ejpam-2985	85	6	a	a	DET
ejpam-2985	85	7	cauchy	cauchy	ADJ
ejpam-2985	85	8	sequence	sequence	NOUN
ejpam-2985	85	9	in	in	ADP
ejpam-2985	85	10	x	x	PUNCT
ejpam-2985	85	11	and	and	CCONJ
ejpam-2985	85	12	suppose	suppose	VERB
ejpam-2985	85	13	that	that	SCONJ
ejpam-2985	85	14	there	there	PRON
ejpam-2985	85	15	is	be	VERB
ejpam-2985	85	16	natural	natural	ADJ
ejpam-2985	85	17	number	number	NOUN
ejpam-2985	85	18	n	n	ADP
ejpam-2985	85	19	such	such	ADJ
ejpam-2985	85	20	that	that	PRON
ejpam-2985	85	21	:	:	PUNCT
ejpam-2985	85	22	(	(	PUNCT
ejpam-2985	85	23	i	i	NOUN
ejpam-2985	85	24	)	)	PUNCT
ejpam-2985	85	25	xn	xn	PROPN
ejpam-2985	86	1	6=	6=	NUM
ejpam-2985	86	2	xm	xm	PROPN
ejpam-2985	86	3	for	for	ADP
ejpam-2985	86	4	all	all	DET
ejpam-2985	86	5	n	n	NOUN
ejpam-2985	86	6	,	,	PUNCT
ejpam-2985	86	7	m	m	VERB
ejpam-2985	86	8	>	>	X
ejpam-2985	86	9	n	n	PROPN
ejpam-2985	86	10	;	;	PUNCT
ejpam-2985	86	11	(	(	PUNCT
ejpam-2985	86	12	ii	ii	NOUN
ejpam-2985	86	13	)	)	PUNCT
ejpam-2985	86	14	xn	xn	PROPN
ejpam-2985	86	15	,	,	PUNCT
ejpam-2985	86	16	x	x	PRON
ejpam-2985	86	17	are	be	AUX
ejpam-2985	86	18	distinct	distinct	ADJ
ejpam-2985	86	19	points	point	NOUN
ejpam-2985	86	20	in	in	ADP
ejpam-2985	86	21	x	x	PUNCT
ejpam-2985	86	22	for	for	ADP
ejpam-2985	86	23	all	all	DET
ejpam-2985	86	24	n	n	CCONJ
ejpam-2985	86	25	>	>	X
ejpam-2985	86	26	n	n	PROPN
ejpam-2985	86	27	;	;	PUNCT
ejpam-2985	86	28	(	(	PUNCT
ejpam-2985	86	29	iii	iii	NOUN
ejpam-2985	86	30	)	)	PUNCT
ejpam-2985	86	31	xn	xn	PROPN
ejpam-2985	86	32	,	,	PUNCT
ejpam-2985	86	33	y	y	PROPN
ejpam-2985	86	34	are	be	AUX
ejpam-2985	86	35	distinct	distinct	ADJ
ejpam-2985	86	36	points	point	NOUN
ejpam-2985	86	37	in	in	ADP
ejpam-2985	86	38	x	x	PUNCT
ejpam-2985	86	39	for	for	ADP
ejpam-2985	86	40	all	all	DET
ejpam-2985	86	41	n	n	CCONJ
ejpam-2985	86	42	>	>	X
ejpam-2985	86	43	n	n	PROPN
ejpam-2985	86	44	;	;	PUNCT
ejpam-2985	86	45	(	(	PUNCT
ejpam-2985	86	46	iv	iv	X
ejpam-2985	86	47	)	)	PUNCT
ejpam-2985	86	48	xn	xn	PUNCT
ejpam-2985	87	1	→	→	PUNCT
ejpam-2985	87	2	x	x	X
ejpam-2985	87	3	and	and	CCONJ
ejpam-2985	87	4	xn	xn	PROPN
ejpam-2985	87	5	→	→	SYM
ejpam-2985	87	6	y	y	PROPN
ejpam-2985	87	7	as	as	ADP
ejpam-2985	87	8	n→∞.	n→∞.	ADJ
ejpam-2985	87	9	then	then	ADV
ejpam-2985	87	10	x	x	X
ejpam-2985	87	11	=	=	PUNCT
ejpam-2985	87	12	y.	y.	NOUN
ejpam-2985	87	13	3	3	NUM
ejpam-2985	87	14	.	.	PUNCT
ejpam-2985	87	15	main	main	ADJ
ejpam-2985	87	16	results	result	NOUN
ejpam-2985	87	17	in	in	ADP
ejpam-2985	87	18	this	this	DET
ejpam-2985	87	19	section	section	NOUN
ejpam-2985	87	20	,	,	PUNCT
ejpam-2985	87	21	we	we	PRON
ejpam-2985	87	22	prove	prove	VERB
ejpam-2985	87	23	banach	banach	NOUN
ejpam-2985	87	24	type	type	NOUN
ejpam-2985	87	25	and	and	CCONJ
ejpam-2985	87	26	kannan	kannan	PROPN
ejpam-2985	87	27	type	type	NOUN
ejpam-2985	87	28	contraction	contraction	NOUN
ejpam-2985	87	29	principles	principle	NOUN
ejpam-2985	87	30	in	in	ADP
ejpam-2985	87	31	cone	cone	NOUN
ejpam-2985	87	32	pentagonal	pentagonal	ADJ
ejpam-2985	87	33	metric	metric	ADJ
ejpam-2985	87	34	spaces	space	NOUN
ejpam-2985	87	35	of	of	ADP
ejpam-2985	87	36	a	a	DET
ejpam-2985	87	37	three	three	NUM
ejpam-2985	87	38	self	self	NOUN
ejpam-2985	87	39	mappings	mapping	NOUN
ejpam-2985	87	40	.	.	PUNCT
ejpam-2985	88	1	we	we	PRON
ejpam-2985	88	2	give	give	VERB
ejpam-2985	88	3	some	some	DET
ejpam-2985	88	4	examples	example	NOUN
ejpam-2985	88	5	to	to	PART
ejpam-2985	88	6	illustrate	illustrate	VERB
ejpam-2985	88	7	the	the	DET
ejpam-2985	88	8	results	result	NOUN
ejpam-2985	88	9	.	.	PUNCT
ejpam-2985	89	1	theorem	theorem	NOUN
ejpam-2985	89	2	1	1	NUM
ejpam-2985	89	3	.	.	PUNCT
ejpam-2985	90	1	let	let	VERB
ejpam-2985	90	2	(	(	PUNCT
ejpam-2985	90	3	x	x	NOUN
ejpam-2985	90	4	,	,	PUNCT
ejpam-2985	90	5	d	d	NOUN
ejpam-2985	90	6	)	)	PUNCT
ejpam-2985	90	7	be	be	AUX
ejpam-2985	90	8	a	a	DET
ejpam-2985	90	9	cone	cone	NOUN
ejpam-2985	90	10	pentagonal	pentagonal	ADJ
ejpam-2985	90	11	metric	metric	ADJ
ejpam-2985	90	12	space	space	NOUN
ejpam-2985	90	13	.	.	PUNCT
ejpam-2985	91	1	suppose	suppose	VERB
ejpam-2985	91	2	the	the	DET
ejpam-2985	91	3	mappings	mapping	NOUN
ejpam-2985	91	4	s	s	PART
ejpam-2985	91	5	,	,	PUNCT
ejpam-2985	91	6	f	f	PROPN
ejpam-2985	91	7	,	,	PUNCT
ejpam-2985	91	8	g	g	NOUN
ejpam-2985	91	9	:	:	PUNCT
ejpam-2985	91	10	x	x	SYM
ejpam-2985	91	11	→	→	PUNCT
ejpam-2985	91	12	x	x	SYM
ejpam-2985	91	13	satisfies	satisfy	VERB
ejpam-2985	91	14	the	the	DET
ejpam-2985	91	15	contractive	contractive	ADJ
ejpam-2985	91	16	condition	condition	NOUN
ejpam-2985	91	17	:	:	PUNCT
ejpam-2985	91	18	d(sx	d(sx	PROPN
ejpam-2985	91	19	,	,	PUNCT
ejpam-2985	91	20	fy	fy	PROPN
ejpam-2985	91	21	)	)	PUNCT
ejpam-2985	91	22	≤	≤	NOUN
ejpam-2985	91	23	ϕ	ϕ	X
ejpam-2985	91	24	(	(	PUNCT
ejpam-2985	91	25	d(gx	d(gx	PROPN
ejpam-2985	91	26	,	,	PUNCT
ejpam-2985	91	27	gy	gy	NOUN
ejpam-2985	91	28	)	)	PUNCT
ejpam-2985	91	29	)	)	PUNCT
ejpam-2985	91	30	,	,	PUNCT
ejpam-2985	91	31	(	(	PUNCT
ejpam-2985	91	32	4	4	X
ejpam-2985	91	33	)	)	PUNCT
ejpam-2985	91	34	for	for	ADP
ejpam-2985	91	35	all	all	DET
ejpam-2985	91	36	x	x	NOUN
ejpam-2985	91	37	,	,	PUNCT
ejpam-2985	91	38	y	y	PROPN
ejpam-2985	91	39	∈	∈	PROPN
ejpam-2985	91	40	x	x	NOUN
ejpam-2985	91	41	,	,	PUNCT
ejpam-2985	91	42	where	where	SCONJ
ejpam-2985	91	43	ϕ	ϕ	PROPN
ejpam-2985	91	44	∈	∈	PROPN
ejpam-2985	91	45	φ	φ	PROPN
ejpam-2985	91	46	.	.	PUNCT
ejpam-2985	91	47	suppose	suppose	VERB
ejpam-2985	91	48	that	that	SCONJ
ejpam-2985	91	49	s(x	s(x	NOUN
ejpam-2985	91	50	)	)	PUNCT
ejpam-2985	91	51	∪	∪	ADP
ejpam-2985	91	52	f(x	f(x	PROPN
ejpam-2985	91	53	)	)	PUNCT
ejpam-2985	91	54	⊆	⊆	NUM
ejpam-2985	91	55	g(x	g(x	NOUN
ejpam-2985	91	56	)	)	PUNCT
ejpam-2985	91	57	,	,	PUNCT
ejpam-2985	91	58	and	and	CCONJ
ejpam-2985	91	59	g(x	g(x	NOUN
ejpam-2985	91	60	)	)	PUNCT
ejpam-2985	91	61	is	be	AUX
ejpam-2985	91	62	a	a	DET
ejpam-2985	91	63	complete	complete	ADJ
ejpam-2985	91	64	subspace	subspace	NOUN
ejpam-2985	91	65	of	of	ADP
ejpam-2985	91	66	x	x	PRON
ejpam-2985	91	67	,	,	PUNCT
ejpam-2985	91	68	then	then	ADV
ejpam-2985	91	69	the	the	DET
ejpam-2985	91	70	mappings	mapping	NOUN
ejpam-2985	91	71	s	s	PART
ejpam-2985	91	72	,	,	PUNCT
ejpam-2985	91	73	f	f	PROPN
ejpam-2985	91	74	and	and	CCONJ
ejpam-2985	91	75	g	g	PROPN
ejpam-2985	91	76	have	have	VERB
ejpam-2985	91	77	a	a	DET
ejpam-2985	91	78	unique	unique	ADJ
ejpam-2985	91	79	point	point	NOUN
ejpam-2985	91	80	of	of	ADP
ejpam-2985	91	81	coincidence	coincidence	NOUN
ejpam-2985	91	82	in	in	ADP
ejpam-2985	91	83	x.	x.	NOUN
ejpam-2985	91	84	moreover	moreover	ADV
ejpam-2985	91	85	,	,	PUNCT
ejpam-2985	91	86	if	if	SCONJ
ejpam-2985	91	87	(	(	PUNCT
ejpam-2985	91	88	s	s	X
ejpam-2985	91	89	,	,	PUNCT
ejpam-2985	91	90	g	g	NOUN
ejpam-2985	91	91	)	)	PUNCT
ejpam-2985	91	92	and	and	CCONJ
ejpam-2985	91	93	(	(	PUNCT
ejpam-2985	91	94	f	f	X
ejpam-2985	91	95	,	,	PUNCT
ejpam-2985	91	96	g	g	NOUN
ejpam-2985	91	97	)	)	PUNCT
ejpam-2985	91	98	are	be	AUX
ejpam-2985	91	99	weakly	weakly	ADV
ejpam-2985	91	100	compatible	compatible	ADJ
ejpam-2985	91	101	then	then	ADV
ejpam-2985	91	102	s	s	PROPN
ejpam-2985	91	103	,	,	PUNCT
ejpam-2985	91	104	f	f	PROPN
ejpam-2985	91	105	and	and	CCONJ
ejpam-2985	91	106	g	g	PROPN
ejpam-2985	91	107	have	have	VERB
ejpam-2985	91	108	a	a	DET
ejpam-2985	91	109	unique	unique	ADJ
ejpam-2985	91	110	common	common	ADJ
ejpam-2985	91	111	fixed	fix	VERB
ejpam-2985	91	112	point	point	NOUN
ejpam-2985	91	113	in	in	ADP
ejpam-2985	91	114	x.	x.	NOUN
ejpam-2985	91	115	proof	proof	NOUN
ejpam-2985	91	116	.	.	PUNCT
ejpam-2985	92	1	let	let	VERB
ejpam-2985	92	2	x0	x0	PROPN
ejpam-2985	92	3	be	be	AUX
ejpam-2985	92	4	an	an	DET
ejpam-2985	92	5	arbitrary	arbitrary	ADJ
ejpam-2985	92	6	point	point	NOUN
ejpam-2985	92	7	in	in	ADP
ejpam-2985	92	8	x.	x.	NOUN
ejpam-2985	92	9	since	since	SCONJ
ejpam-2985	92	10	s(x	s(x	PROPN
ejpam-2985	92	11	)	)	PUNCT
ejpam-2985	92	12	∪	∪	ADP
ejpam-2985	92	13	f(x	f(x	PROPN
ejpam-2985	92	14	)	)	PUNCT
ejpam-2985	92	15	⊆	⊆	NUM
ejpam-2985	92	16	g(x	g(x	NOUN
ejpam-2985	92	17	)	)	PUNCT
ejpam-2985	92	18	,	,	PUNCT
ejpam-2985	92	19	we	we	PRON
ejpam-2985	92	20	can	can	AUX
ejpam-2985	92	21	choose	choose	VERB
ejpam-2985	92	22	x1	x1	PROPN
ejpam-2985	92	23	∈	∈	PROPN
ejpam-2985	92	24	x	x	PUNCT
ejpam-2985	92	25	such	such	ADJ
ejpam-2985	92	26	that	that	SCONJ
ejpam-2985	92	27	gx1	gx1	PROPN
ejpam-2985	92	28	=	=	PUNCT
ejpam-2985	92	29	sx0	sx0	PROPN
ejpam-2985	92	30	.	.	PUNCT
ejpam-2985	93	1	also	also	ADV
ejpam-2985	93	2	we	we	PRON
ejpam-2985	93	3	can	can	AUX
ejpam-2985	93	4	choose	choose	VERB
ejpam-2985	93	5	x2	x2	PROPN
ejpam-2985	93	6	∈	∈	PROPN
ejpam-2985	93	7	x	x	PUNCT
ejpam-2985	93	8	such	such	ADJ
ejpam-2985	93	9	that	that	SCONJ
ejpam-2985	93	10	gx2	gx2	NOUN
ejpam-2985	93	11	=	=	PROPN
ejpam-2985	93	12	fx1	fx1	PROPN
ejpam-2985	93	13	.	.	PUNCT
ejpam-2985	94	1	continuing	continue	VERB
ejpam-2985	94	2	this	this	DET
ejpam-2985	94	3	process	process	NOUN
ejpam-2985	94	4	,	,	PUNCT
ejpam-2985	94	5	having	having	AUX
ejpam-2985	94	6	chosen	choose	VERB
ejpam-2985	94	7	xn	xn	PROPN
ejpam-2985	94	8	in	in	ADP
ejpam-2985	94	9	x	x	SYM
ejpam-2985	94	10	,	,	PUNCT
ejpam-2985	94	11	we	we	PRON
ejpam-2985	94	12	obtain	obtain	VERB
ejpam-2985	94	13	xn+1	xn+1	NUM
ejpam-2985	94	14	such	such	ADJ
ejpam-2985	94	15	that	that	DET
ejpam-2985	94	16	gxn+1	gxn+1	PROPN
ejpam-2985	94	17	=	=	SYM
ejpam-2985	94	18	sxn	sxn	NOUN
ejpam-2985	94	19	and	and	CCONJ
ejpam-2985	94	20	gxn+2	gxn+2	X
ejpam-2985	94	21	=	=	SYM
ejpam-2985	94	22	fxn+1	fxn+1	PROPN
ejpam-2985	94	23	,	,	PUNCT
ejpam-2985	94	24	for	for	ADP
ejpam-2985	94	25	all	all	DET
ejpam-2985	94	26	n	n	NOUN
ejpam-2985	94	27	=	=	SYM
ejpam-2985	94	28	0	0	NUM
ejpam-2985	94	29	,	,	PUNCT
ejpam-2985	94	30	1	1	NUM
ejpam-2985	94	31	,	,	PUNCT
ejpam-2985	94	32	2	2	NUM
ejpam-2985	94	33	,	,	PUNCT
ejpam-2985	94	34	·	·	PUNCT
ejpam-2985	94	35	·	·	PUNCT
ejpam-2985	94	36	·	·	PUNCT
ejpam-2985	94	37	.	.	PUNCT
ejpam-2985	95	1	a.	a.	PROPN
ejpam-2985	95	2	auwalu	auwalu	PROPN
ejpam-2985	95	3	,	,	PUNCT
ejpam-2985	95	4	e.	e.	PROPN
ejpam-2985	95	5	hınçal	hınçal	PROPN
ejpam-2985	95	6	/	/	SYM
ejpam-2985	95	7	eur	eur	PROPN
ejpam-2985	95	8	.	.	PUNCT
ejpam-2985	96	1	j.	j.	PROPN
ejpam-2985	96	2	pure	pure	PROPN
ejpam-2985	96	3	appl	appl	PROPN
ejpam-2985	96	4	.	.	PROPN
ejpam-2985	96	5	math	math	PROPN
ejpam-2985	96	6	,	,	PUNCT
ejpam-2985	96	7	10	10	NUM
ejpam-2985	96	8	(	(	PUNCT
ejpam-2985	96	9	3	3	NUM
ejpam-2985	96	10	)	)	PUNCT
ejpam-2985	96	11	(	(	PUNCT
ejpam-2985	96	12	2017	2017	NUM
ejpam-2985	96	13	)	)	PUNCT
ejpam-2985	96	14	,	,	PUNCT
ejpam-2985	96	15	473	473	NUM
ejpam-2985	96	16	-	-	SYM
ejpam-2985	96	17	487	487	NUM
ejpam-2985	96	18	477	477	NUM
ejpam-2985	96	19	if	if	SCONJ
ejpam-2985	96	20	gxn	gxn	PROPN
ejpam-2985	96	21	=	=	SYM
ejpam-2985	96	22	gxn+1	gxn+1	PROPN
ejpam-2985	96	23	,	,	PUNCT
ejpam-2985	96	24	then	then	ADV
ejpam-2985	96	25	gxn	gxn	PROPN
ejpam-2985	96	26	=	=	SYM
ejpam-2985	96	27	sxn	sxn	NOUN
ejpam-2985	96	28	=	=	PUNCT
ejpam-2985	96	29	fxn	fxn	NOUN
ejpam-2985	96	30	,	,	PUNCT
ejpam-2985	96	31	and	and	CCONJ
ejpam-2985	96	32	xn	xn	PROPN
ejpam-2985	96	33	is	be	AUX
ejpam-2985	96	34	a	a	DET
ejpam-2985	96	35	coincidence	coincidence	NOUN
ejpam-2985	96	36	point	point	NOUN
ejpam-2985	96	37	of	of	ADP
ejpam-2985	96	38	s	s	PROPN
ejpam-2985	96	39	,	,	PUNCT
ejpam-2985	96	40	f	f	PROPN
ejpam-2985	96	41	and	and	CCONJ
ejpam-2985	96	42	g.	g.	PROPN
ejpam-2985	96	43	hence	hence	ADV
ejpam-2985	96	44	,	,	PUNCT
ejpam-2985	96	45	we	we	PRON
ejpam-2985	96	46	assume	assume	VERB
ejpam-2985	96	47	that	that	SCONJ
ejpam-2985	96	48	xn	xn	PROPN
ejpam-2985	96	49	6=	6=	NUM
ejpam-2985	96	50	xn+1	xn+1	NUM
ejpam-2985	96	51	for	for	ADP
ejpam-2985	96	52	all	all	PRON
ejpam-2985	96	53	n	n	DET
ejpam-2985	96	54	∈	∈	PROPN
ejpam-2985	96	55	n.	n.	NOUN
ejpam-2985	96	56	then	then	ADV
ejpam-2985	96	57	,	,	PUNCT
ejpam-2985	96	58	from	from	ADP
ejpam-2985	96	59	(	(	PUNCT
ejpam-2985	96	60	4	4	NUM
ejpam-2985	96	61	)	)	PUNCT
ejpam-2985	96	62	,	,	PUNCT
ejpam-2985	96	63	it	it	PRON
ejpam-2985	96	64	follows	follow	VERB
ejpam-2985	96	65	that	that	SCONJ
ejpam-2985	96	66	d(gxn	d(gxn	VERB
ejpam-2985	96	67	,	,	PUNCT
ejpam-2985	96	68	gxn+1	gxn+1	PROPN
ejpam-2985	96	69	)	)	PUNCT
ejpam-2985	97	1	=	=	SYM
ejpam-2985	97	2	ϕ	ϕ	PROPN
ejpam-2985	97	3	(	(	PUNCT
ejpam-2985	97	4	d(sxn−1	d(sxn−1	PROPN
ejpam-2985	97	5	,	,	PUNCT
ejpam-2985	97	6	fxn	fxn	NOUN
ejpam-2985	97	7	)	)	PUNCT
ejpam-2985	97	8	)	)	PUNCT
ejpam-2985	98	1	≤	≤	NOUN
ejpam-2985	98	2	ϕ	ϕ	X
ejpam-2985	98	3	(	(	PUNCT
ejpam-2985	98	4	d(gxn−1	d(gxn−1	PROPN
ejpam-2985	98	5	,	,	PUNCT
ejpam-2985	98	6	gxn	gxn	PROPN
ejpam-2985	98	7	)	)	PUNCT
ejpam-2985	98	8	)	)	PUNCT
ejpam-2985	98	9	≤	≤	ADV
ejpam-2985	98	10	ϕ2	ϕ2	ADV
ejpam-2985	98	11	(	(	PUNCT
ejpam-2985	98	12	d(gxn−2	d(gxn−2	PROPN
ejpam-2985	98	13	,	,	PUNCT
ejpam-2985	98	14	gxn−1	gxn−1	PROPN
ejpam-2985	98	15	)	)	PUNCT
ejpam-2985	98	16	)	)	PUNCT
ejpam-2985	98	17	...	...	PUNCT
ejpam-2985	99	1	≤	≤	NUM
ejpam-2985	99	2	ϕn	ϕn	X
ejpam-2985	99	3	(	(	PUNCT
ejpam-2985	99	4	d(gx0	d(gx0	PROPN
ejpam-2985	99	5	,	,	PUNCT
ejpam-2985	99	6	gx1	gx1	PROPN
ejpam-2985	99	7	)	)	PUNCT
ejpam-2985	99	8	)	)	PUNCT
ejpam-2985	99	9	.	.	PUNCT
ejpam-2985	100	1	(	(	PUNCT
ejpam-2985	100	2	5	5	X
ejpam-2985	100	3	)	)	PUNCT
ejpam-2985	100	4	in	in	ADP
ejpam-2985	100	5	similar	similar	ADJ
ejpam-2985	100	6	way	way	NOUN
ejpam-2985	100	7	,	,	PUNCT
ejpam-2985	100	8	it	it	PRON
ejpam-2985	100	9	again	again	ADV
ejpam-2985	100	10	follows	follow	VERB
ejpam-2985	100	11	that	that	PRON
ejpam-2985	100	12	d(gxn	d(gxn	VERB
ejpam-2985	100	13	,	,	PUNCT
ejpam-2985	100	14	gxn+2	gxn+2	PROPN
ejpam-2985	100	15	)	)	PUNCT
ejpam-2985	100	16	≤	≤	NOUN
ejpam-2985	101	1	ϕn	ϕn	X
ejpam-2985	101	2	(	(	PUNCT
ejpam-2985	101	3	d(gx0	d(gx0	PROPN
ejpam-2985	101	4	,	,	PUNCT
ejpam-2985	101	5	gx2	gx2	PROPN
ejpam-2985	101	6	)	)	PUNCT
ejpam-2985	101	7	)	)	PUNCT
ejpam-2985	101	8	,	,	PUNCT
ejpam-2985	101	9	(	(	PUNCT
ejpam-2985	101	10	6	6	X
ejpam-2985	101	11	)	)	PUNCT
ejpam-2985	101	12	d(gxn	d(gxn	PROPN
ejpam-2985	101	13	,	,	PUNCT
ejpam-2985	101	14	gxn+3	gxn+3	NOUN
ejpam-2985	101	15	)	)	PUNCT
ejpam-2985	101	16	≤	≤	PUNCT
ejpam-2985	102	1	ϕn	ϕn	X
ejpam-2985	102	2	(	(	PUNCT
ejpam-2985	102	3	d(gx0	d(gx0	PROPN
ejpam-2985	102	4	,	,	PUNCT
ejpam-2985	102	5	gx3	gx3	NOUN
ejpam-2985	102	6	)	)	PUNCT
ejpam-2985	102	7	)	)	PUNCT
ejpam-2985	102	8	.	.	PUNCT
ejpam-2985	103	1	(	(	PUNCT
ejpam-2985	103	2	7	7	X
ejpam-2985	103	3	)	)	PUNCT
ejpam-2985	103	4	similarly	similarly	ADV
ejpam-2985	103	5	,	,	PUNCT
ejpam-2985	103	6	for	for	ADP
ejpam-2985	103	7	k	k	PROPN
ejpam-2985	103	8	=	=	SYM
ejpam-2985	103	9	1	1	NUM
ejpam-2985	103	10	,	,	PUNCT
ejpam-2985	103	11	2	2	NUM
ejpam-2985	103	12	,	,	PUNCT
ejpam-2985	103	13	3	3	NUM
ejpam-2985	103	14	,	,	PUNCT
ejpam-2985	103	15	·	·	PUNCT
ejpam-2985	103	16	·	·	PUNCT
ejpam-2985	103	17	·	·	PUNCT
ejpam-2985	103	18	,	,	PUNCT
ejpam-2985	103	19	it	it	PRON
ejpam-2985	103	20	further	far	ADV
ejpam-2985	103	21	follows	follow	VERB
ejpam-2985	103	22	that	that	SCONJ
ejpam-2985	103	23	d(gxn	d(gxn	VERB
ejpam-2985	103	24	,	,	PUNCT
ejpam-2985	103	25	gxn+3k+1	gxn+3k+1	NOUN
ejpam-2985	103	26	)	)	PUNCT
ejpam-2985	103	27	≤	≤	NOUN
ejpam-2985	104	1	ϕn	ϕn	X
ejpam-2985	104	2	(	(	PUNCT
ejpam-2985	104	3	d(gx0	d(gx0	PROPN
ejpam-2985	104	4	,	,	PUNCT
ejpam-2985	104	5	gx3k+1	gx3k+1	PROPN
ejpam-2985	104	6	)	)	PUNCT
ejpam-2985	104	7	)	)	PUNCT
ejpam-2985	104	8	,	,	PUNCT
ejpam-2985	104	9	(	(	PUNCT
ejpam-2985	104	10	8)	8)	NUM
ejpam-2985	104	11	d(gxn	d(gxn	PROPN
ejpam-2985	104	12	,	,	PUNCT
ejpam-2985	104	13	gxn+3k+2	gxn+3k+2	NOUN
ejpam-2985	104	14	)	)	PUNCT
ejpam-2985	104	15	≤	≤	NOUN
ejpam-2985	105	1	ϕn	ϕn	X
ejpam-2985	105	2	(	(	PUNCT
ejpam-2985	105	3	d(gx0	d(gx0	PROPN
ejpam-2985	105	4	,	,	PUNCT
ejpam-2985	105	5	gx3k+2	gx3k+2	NOUN
ejpam-2985	105	6	)	)	PUNCT
ejpam-2985	105	7	)	)	PUNCT
ejpam-2985	105	8	,	,	PUNCT
ejpam-2985	105	9	(	(	PUNCT
ejpam-2985	105	10	9	9	X
ejpam-2985	105	11	)	)	PUNCT
ejpam-2985	105	12	d(gxn	d(gxn	PROPN
ejpam-2985	105	13	,	,	PUNCT
ejpam-2985	105	14	gxn+3k+3	gxn+3k+3	ADJ
ejpam-2985	105	15	)	)	PUNCT
ejpam-2985	105	16	≤	≤	NOUN
ejpam-2985	106	1	ϕn	ϕn	X
ejpam-2985	106	2	(	(	PUNCT
ejpam-2985	106	3	d(gx0	d(gx0	PROPN
ejpam-2985	106	4	,	,	PUNCT
ejpam-2985	106	5	gx3k+3	gx3k+3	PROPN
ejpam-2985	106	6	)	)	PUNCT
ejpam-2985	106	7	)	)	PUNCT
ejpam-2985	106	8	.	.	PUNCT
ejpam-2985	107	1	(	(	PUNCT
ejpam-2985	107	2	10	10	NUM
ejpam-2985	107	3	)	)	PUNCT
ejpam-2985	107	4	by	by	ADP
ejpam-2985	107	5	pentagonal	pentagonal	ADJ
ejpam-2985	107	6	property	property	NOUN
ejpam-2985	107	7	and	and	CCONJ
ejpam-2985	107	8	(	(	PUNCT
ejpam-2985	107	9	5	5	NUM
ejpam-2985	107	10	)	)	PUNCT
ejpam-2985	107	11	,	,	PUNCT
ejpam-2985	107	12	we	we	PRON
ejpam-2985	107	13	have	have	VERB
ejpam-2985	107	14	d(gx0	d(gx0	PROPN
ejpam-2985	107	15	,	,	PUNCT
ejpam-2985	107	16	gx4	gx4	ADJ
ejpam-2985	107	17	)	)	PUNCT
ejpam-2985	107	18	≤	≤	NOUN
ejpam-2985	108	1	d(gx0	d(gx0	PROPN
ejpam-2985	108	2	,	,	PUNCT
ejpam-2985	108	3	gx1	gx1	PROPN
ejpam-2985	108	4	)	)	PUNCT
ejpam-2985	109	1	+	+	CCONJ
ejpam-2985	109	2	d(gx1	d(gx1	PROPN
ejpam-2985	109	3	,	,	PUNCT
ejpam-2985	109	4	gx2	gx2	PROPN
ejpam-2985	109	5	)	)	PUNCT
ejpam-2985	109	6	+	+	CCONJ
ejpam-2985	110	1	d(gx2	d(gx2	PROPN
ejpam-2985	110	2	,	,	PUNCT
ejpam-2985	110	3	gx3	gx3	NOUN
ejpam-2985	110	4	)	)	PUNCT
ejpam-2985	111	1	+	+	CCONJ
ejpam-2985	112	1	d(gx3	d(gx3	PROPN
ejpam-2985	112	2	,	,	PUNCT
ejpam-2985	112	3	gx4	gx4	NOUN
ejpam-2985	112	4	)	)	PUNCT
ejpam-2985	112	5	≤	≤	NOUN
ejpam-2985	113	1	d(gx0	d(gx0	PROPN
ejpam-2985	113	2	,	,	PUNCT
ejpam-2985	113	3	gx1	gx1	PROPN
ejpam-2985	113	4	)	)	PUNCT
ejpam-2985	114	1	+	+	CCONJ
ejpam-2985	114	2	ϕ	ϕ	X
ejpam-2985	114	3	(	(	PUNCT
ejpam-2985	114	4	d(gx0	d(gx0	PROPN
ejpam-2985	114	5	,	,	PUNCT
ejpam-2985	114	6	gx1	gx1	PROPN
ejpam-2985	114	7	)	)	PUNCT
ejpam-2985	114	8	)	)	PUNCT
ejpam-2985	115	1	+	+	CCONJ
ejpam-2985	115	2	ϕ2	ϕ2	ADV
ejpam-2985	115	3	(	(	PUNCT
ejpam-2985	115	4	d(gx0	d(gx0	PROPN
ejpam-2985	115	5	,	,	PUNCT
ejpam-2985	115	6	gx1	gx1	PROPN
ejpam-2985	115	7	)	)	PUNCT
ejpam-2985	115	8	)	)	PUNCT
ejpam-2985	116	1	+	+	CCONJ
ejpam-2985	116	2	ϕ3	ϕ3	PROPN
ejpam-2985	116	3	(	(	PUNCT
ejpam-2985	116	4	d(gx0	d(gx0	PROPN
ejpam-2985	116	5	,	,	PUNCT
ejpam-2985	116	6	gx1	gx1	PROPN
ejpam-2985	116	7	)	)	PUNCT
ejpam-2985	116	8	)	)	PUNCT
ejpam-2985	116	9	≤	≤	NUM
ejpam-2985	117	1	3∑	3∑	NUM
ejpam-2985	117	2	i=0	i=0	PROPN
ejpam-2985	117	3	ϕi	ϕi	X
ejpam-2985	117	4	(	(	PUNCT
ejpam-2985	117	5	d(gx0	d(gx0	PROPN
ejpam-2985	117	6	,	,	PUNCT
ejpam-2985	117	7	gx1	gx1	PROPN
ejpam-2985	117	8	)	)	PUNCT
ejpam-2985	117	9	)	)	PUNCT
ejpam-2985	117	10	,	,	PUNCT
ejpam-2985	117	11	and	and	CCONJ
ejpam-2985	117	12	d(gx0	d(gx0	ADJ
ejpam-2985	117	13	,	,	PUNCT
ejpam-2985	117	14	gx7	gx7	NOUN
ejpam-2985	117	15	)	)	PUNCT
ejpam-2985	117	16	≤	≤	NOUN
ejpam-2985	117	17	d(gx0	d(gx0	PROPN
ejpam-2985	117	18	,	,	PUNCT
ejpam-2985	117	19	gx1	gx1	PROPN
ejpam-2985	117	20	)	)	PUNCT
ejpam-2985	117	21	+	+	CCONJ
ejpam-2985	118	1	d(gx1	d(gx1	PROPN
ejpam-2985	118	2	,	,	PUNCT
ejpam-2985	118	3	gx2	gx2	PROPN
ejpam-2985	118	4	)	)	PUNCT
ejpam-2985	118	5	+	+	CCONJ
ejpam-2985	119	1	d(gx2	d(gx2	PROPN
ejpam-2985	119	2	,	,	PUNCT
ejpam-2985	119	3	gx3	gx3	NOUN
ejpam-2985	119	4	)	)	PUNCT
ejpam-2985	120	1	+	+	CCONJ
ejpam-2985	121	1	d(gx3	d(gx3	PROPN
ejpam-2985	121	2	,	,	PUNCT
ejpam-2985	121	3	gx4	gx4	NOUN
ejpam-2985	121	4	)	)	PUNCT
ejpam-2985	121	5	+	+	CCONJ
ejpam-2985	121	6	d(gx4	d(gx4	NOUN
ejpam-2985	121	7	,	,	PUNCT
ejpam-2985	121	8	gx5	gx5	X
ejpam-2985	121	9	)	)	PUNCT
ejpam-2985	121	10	+	+	SYM
ejpam-2985	121	11	d(gx5	d(gx5	PROPN
ejpam-2985	121	12	,	,	PUNCT
ejpam-2985	121	13	gx6	gx6	PROPN
ejpam-2985	121	14	)	)	PUNCT
ejpam-2985	122	1	+	+	X
ejpam-2985	122	2	d(gx6	d(gx6	PROPN
ejpam-2985	122	3	,	,	PUNCT
ejpam-2985	122	4	gx7	gx7	NOUN
ejpam-2985	122	5	)	)	PUNCT
ejpam-2985	122	6	≤	≤	NUM
ejpam-2985	122	7	6∑	6∑	NUM
ejpam-2985	123	1	i=0	i=0	PUNCT
ejpam-2985	123	2	ϕi	ϕi	X
ejpam-2985	123	3	(	(	PUNCT
ejpam-2985	123	4	d(gx0	d(gx0	PROPN
ejpam-2985	123	5	,	,	PUNCT
ejpam-2985	123	6	gx1	gx1	PROPN
ejpam-2985	123	7	)	)	PUNCT
ejpam-2985	123	8	)	)	PUNCT
ejpam-2985	123	9	.	.	PUNCT
ejpam-2985	124	1	now	now	ADV
ejpam-2985	124	2	,	,	PUNCT
ejpam-2985	124	3	by	by	ADP
ejpam-2985	124	4	induction	induction	NOUN
ejpam-2985	124	5	,	,	PUNCT
ejpam-2985	124	6	we	we	PRON
ejpam-2985	124	7	obtain	obtain	VERB
ejpam-2985	124	8	for	for	ADP
ejpam-2985	124	9	each	each	PRON
ejpam-2985	124	10	k	k	NOUN
ejpam-2985	125	1	=	=	SYM
ejpam-2985	125	2	1	1	NUM
ejpam-2985	125	3	,	,	PUNCT
ejpam-2985	125	4	2	2	NUM
ejpam-2985	125	5	,	,	PUNCT
ejpam-2985	125	6	3	3	NUM
ejpam-2985	125	7	,	,	PUNCT
ejpam-2985	125	8	·	·	PUNCT
ejpam-2985	125	9	·	·	PUNCT
ejpam-2985	125	10	·	·	PUNCT
ejpam-2985	125	11	d(gx0	d(gx0	ADJ
ejpam-2985	125	12	,	,	PUNCT
ejpam-2985	125	13	gx3k+1	gx3k+1	NOUN
ejpam-2985	125	14	)	)	PUNCT
ejpam-2985	125	15	≤	≤	NOUN
ejpam-2985	126	1	3k∑	3k∑	NUM
ejpam-2985	126	2	i=0	i=0	PROPN
ejpam-2985	126	3	ϕi	ϕi	X
ejpam-2985	126	4	(	(	PUNCT
ejpam-2985	126	5	d(gx0	d(gx0	PROPN
ejpam-2985	126	6	,	,	PUNCT
ejpam-2985	126	7	gx1	gx1	PROPN
ejpam-2985	126	8	)	)	PUNCT
ejpam-2985	126	9	)	)	PUNCT
ejpam-2985	126	10	.	.	PUNCT
ejpam-2985	127	1	(	(	PUNCT
ejpam-2985	127	2	11	11	NUM
ejpam-2985	127	3	)	)	PUNCT
ejpam-2985	127	4	also	also	ADV
ejpam-2985	127	5	,	,	PUNCT
ejpam-2985	127	6	using	use	VERB
ejpam-2985	127	7	(	(	PUNCT
ejpam-2985	127	8	5	5	NUM
ejpam-2985	127	9	)	)	PUNCT
ejpam-2985	127	10	,	,	PUNCT
ejpam-2985	127	11	(	(	PUNCT
ejpam-2985	127	12	6	6	NUM
ejpam-2985	127	13	)	)	PUNCT
ejpam-2985	127	14	,	,	PUNCT
ejpam-2985	127	15	and	and	CCONJ
ejpam-2985	127	16	pentagonal	pentagonal	ADJ
ejpam-2985	127	17	property	property	NOUN
ejpam-2985	127	18	,	,	PUNCT
ejpam-2985	127	19	we	we	PRON
ejpam-2985	127	20	have	have	VERB
ejpam-2985	127	21	that	that	DET
ejpam-2985	127	22	d(gx0	d(gx0	PROPN
ejpam-2985	127	23	,	,	PUNCT
ejpam-2985	127	24	gx5	gx5	PROPN
ejpam-2985	127	25	)	)	PUNCT
ejpam-2985	127	26	≤	≤	NUM
ejpam-2985	128	1	2∑	2∑	X
ejpam-2985	128	2	i=0	i=0	PUNCT
ejpam-2985	128	3	ϕi	ϕi	X
ejpam-2985	128	4	(	(	PUNCT
ejpam-2985	128	5	d(gx0	d(gx0	PROPN
ejpam-2985	128	6	,	,	PUNCT
ejpam-2985	128	7	gx1	gx1	PROPN
ejpam-2985	128	8	)	)	PUNCT
ejpam-2985	128	9	)	)	PUNCT
ejpam-2985	129	1	+	+	CCONJ
ejpam-2985	129	2	ϕ3	ϕ3	PROPN
ejpam-2985	129	3	(	(	PUNCT
ejpam-2985	129	4	d(gx0	d(gx0	PROPN
ejpam-2985	129	5	,	,	PUNCT
ejpam-2985	129	6	gx2	gx2	PROPN
ejpam-2985	129	7	)	)	PUNCT
ejpam-2985	129	8	)	)	PUNCT
ejpam-2985	129	9	,	,	PUNCT
ejpam-2985	129	10	a.	a.	NOUN
ejpam-2985	129	11	auwalu	auwalu	PROPN
ejpam-2985	129	12	,	,	PUNCT
ejpam-2985	129	13	e.	e.	PROPN
ejpam-2985	129	14	hınçal	hınçal	PROPN
ejpam-2985	129	15	/	/	SYM
ejpam-2985	129	16	eur	eur	PROPN
ejpam-2985	129	17	.	.	PUNCT
ejpam-2985	130	1	j.	j.	PROPN
ejpam-2985	130	2	pure	pure	PROPN
ejpam-2985	130	3	appl	appl	PROPN
ejpam-2985	130	4	.	.	PROPN
ejpam-2985	130	5	math	math	PROPN
ejpam-2985	130	6	,	,	PUNCT
ejpam-2985	130	7	10	10	NUM
ejpam-2985	130	8	(	(	PUNCT
ejpam-2985	130	9	3	3	NUM
ejpam-2985	130	10	)	)	PUNCT
ejpam-2985	130	11	(	(	PUNCT
ejpam-2985	130	12	2017	2017	NUM
ejpam-2985	130	13	)	)	PUNCT
ejpam-2985	130	14	,	,	PUNCT
ejpam-2985	130	15	473	473	NUM
ejpam-2985	130	16	-	-	SYM
ejpam-2985	130	17	487	487	NUM
ejpam-2985	130	18	478	478	NUM
ejpam-2985	130	19	and	and	CCONJ
ejpam-2985	130	20	d(gx0	d(gx0	ADJ
ejpam-2985	130	21	,	,	PUNCT
ejpam-2985	130	22	gx8	gx8	NOUN
ejpam-2985	130	23	)	)	PUNCT
ejpam-2985	130	24	≤	≤	NOUN
ejpam-2985	131	1	5∑	5∑	ADJ
ejpam-2985	131	2	i=0	i=0	PROPN
ejpam-2985	131	3	ϕi	ϕi	X
ejpam-2985	131	4	(	(	PUNCT
ejpam-2985	131	5	d(gx0	d(gx0	PROPN
ejpam-2985	131	6	,	,	PUNCT
ejpam-2985	131	7	gx1	gx1	PROPN
ejpam-2985	131	8	)	)	PUNCT
ejpam-2985	131	9	)	)	PUNCT
ejpam-2985	132	1	+	+	CCONJ
ejpam-2985	132	2	ϕ6	ϕ6	PROPN
ejpam-2985	132	3	(	(	PUNCT
ejpam-2985	132	4	d(gx0	d(gx0	PROPN
ejpam-2985	132	5	,	,	PUNCT
ejpam-2985	132	6	gx2	gx2	PROPN
ejpam-2985	132	7	)	)	PUNCT
ejpam-2985	132	8	)	)	PUNCT
ejpam-2985	132	9	.	.	PUNCT
ejpam-2985	133	1	by	by	ADP
ejpam-2985	133	2	induction	induction	NOUN
ejpam-2985	133	3	,	,	PUNCT
ejpam-2985	133	4	we	we	PRON
ejpam-2985	133	5	obtain	obtain	VERB
ejpam-2985	133	6	for	for	ADP
ejpam-2985	133	7	each	each	PRON
ejpam-2985	133	8	k	k	NOUN
ejpam-2985	134	1	=	=	SYM
ejpam-2985	134	2	1	1	NUM
ejpam-2985	134	3	,	,	PUNCT
ejpam-2985	134	4	2	2	NUM
ejpam-2985	134	5	,	,	PUNCT
ejpam-2985	134	6	3	3	NUM
ejpam-2985	134	7	,	,	PUNCT
ejpam-2985	134	8	·	·	PUNCT
ejpam-2985	134	9	·	·	PUNCT
ejpam-2985	134	10	·	·	PUNCT
ejpam-2985	134	11	d(gx0	d(gx0	ADJ
ejpam-2985	134	12	,	,	PUNCT
ejpam-2985	134	13	gx3k+2	gx3k+2	NOUN
ejpam-2985	134	14	)	)	PUNCT
ejpam-2985	134	15	≤	≤	NOUN
ejpam-2985	135	1	3k−1∑	3k−1∑	NUM
ejpam-2985	135	2	i=0	i=0	PUNCT
ejpam-2985	135	3	ϕi	ϕi	X
ejpam-2985	135	4	(	(	PUNCT
ejpam-2985	135	5	d(gx0	d(gx0	PROPN
ejpam-2985	135	6	,	,	PUNCT
ejpam-2985	135	7	gx1	gx1	PROPN
ejpam-2985	135	8	)	)	PUNCT
ejpam-2985	135	9	)	)	PUNCT
ejpam-2985	136	1	+	+	CCONJ
ejpam-2985	136	2	ϕ3k	ϕ3k	PRON
ejpam-2985	136	3	(	(	PUNCT
ejpam-2985	136	4	d(gx0	d(gx0	PROPN
ejpam-2985	136	5	,	,	PUNCT
ejpam-2985	136	6	gx2	gx2	PROPN
ejpam-2985	136	7	)	)	PUNCT
ejpam-2985	136	8	)	)	PUNCT
ejpam-2985	136	9	.	.	PUNCT
ejpam-2985	137	1	(	(	PUNCT
ejpam-2985	137	2	12	12	NUM
ejpam-2985	137	3	)	)	PUNCT
ejpam-2985	137	4	again	again	ADV
ejpam-2985	137	5	,	,	PUNCT
ejpam-2985	137	6	using	use	VERB
ejpam-2985	137	7	(	(	PUNCT
ejpam-2985	137	8	5	5	NUM
ejpam-2985	137	9	)	)	PUNCT
ejpam-2985	137	10	,	,	PUNCT
ejpam-2985	137	11	(	(	PUNCT
ejpam-2985	137	12	7	7	NUM
ejpam-2985	137	13	)	)	PUNCT
ejpam-2985	137	14	,	,	PUNCT
ejpam-2985	137	15	and	and	CCONJ
ejpam-2985	137	16	pentagonal	pentagonal	ADJ
ejpam-2985	137	17	property	property	NOUN
ejpam-2985	137	18	,	,	PUNCT
ejpam-2985	137	19	we	we	PRON
ejpam-2985	137	20	have	have	VERB
ejpam-2985	137	21	that	that	DET
ejpam-2985	137	22	d(gx0	d(gx0	PROPN
ejpam-2985	137	23	,	,	PUNCT
ejpam-2985	137	24	gx6	gx6	PROPN
ejpam-2985	137	25	)	)	PUNCT
ejpam-2985	137	26	≤	≤	NUM
ejpam-2985	138	1	2∑	2∑	X
ejpam-2985	138	2	i=0	i=0	PUNCT
ejpam-2985	138	3	ϕi	ϕi	X
ejpam-2985	138	4	(	(	PUNCT
ejpam-2985	138	5	d(gx0	d(gx0	PROPN
ejpam-2985	138	6	,	,	PUNCT
ejpam-2985	138	7	gx1	gx1	PROPN
ejpam-2985	138	8	)	)	PUNCT
ejpam-2985	138	9	)	)	PUNCT
ejpam-2985	139	1	+	+	CCONJ
ejpam-2985	139	2	ϕ3	ϕ3	PROPN
ejpam-2985	139	3	(	(	PUNCT
ejpam-2985	139	4	d(gx0	d(gx0	PROPN
ejpam-2985	139	5	,	,	PUNCT
ejpam-2985	139	6	gx3	gx3	NOUN
ejpam-2985	139	7	)	)	PUNCT
ejpam-2985	139	8	)	)	PUNCT
ejpam-2985	139	9	,	,	PUNCT
ejpam-2985	139	10	and	and	CCONJ
ejpam-2985	139	11	d(gx0	d(gx0	ADJ
ejpam-2985	139	12	,	,	PUNCT
ejpam-2985	139	13	gx9	gx9	PROPN
ejpam-2985	139	14	)	)	PUNCT
ejpam-2985	139	15	≤	≤	NOUN
ejpam-2985	139	16	5∑	5∑	PROPN
ejpam-2985	139	17	i=0	i=0	PROPN
ejpam-2985	139	18	ϕi	ϕi	X
ejpam-2985	139	19	(	(	PUNCT
ejpam-2985	139	20	d(gx0	d(gx0	PROPN
ejpam-2985	139	21	,	,	PUNCT
ejpam-2985	139	22	gx1	gx1	PROPN
ejpam-2985	139	23	)	)	PUNCT
ejpam-2985	139	24	)	)	PUNCT
ejpam-2985	140	1	+	+	CCONJ
ejpam-2985	140	2	ϕ6	ϕ6	PROPN
ejpam-2985	140	3	(	(	PUNCT
ejpam-2985	140	4	d(gx0	d(gx0	PROPN
ejpam-2985	140	5	,	,	PUNCT
ejpam-2985	140	6	gx3	gx3	NOUN
ejpam-2985	140	7	)	)	PUNCT
ejpam-2985	140	8	)	)	PUNCT
ejpam-2985	140	9	.	.	PUNCT
ejpam-2985	141	1	by	by	ADP
ejpam-2985	141	2	induction	induction	NOUN
ejpam-2985	141	3	,	,	PUNCT
ejpam-2985	141	4	we	we	PRON
ejpam-2985	141	5	obtain	obtain	VERB
ejpam-2985	141	6	for	for	ADP
ejpam-2985	141	7	each	each	PRON
ejpam-2985	141	8	k	k	NOUN
ejpam-2985	142	1	=	=	SYM
ejpam-2985	142	2	1	1	NUM
ejpam-2985	142	3	,	,	PUNCT
ejpam-2985	142	4	2	2	NUM
ejpam-2985	142	5	,	,	PUNCT
ejpam-2985	142	6	3	3	NUM
ejpam-2985	142	7	,	,	PUNCT
ejpam-2985	142	8	·	·	PUNCT
ejpam-2985	142	9	·	·	PUNCT
ejpam-2985	143	1	·	·	PUNCT
ejpam-2985	143	2	d(gx0	d(gx0	ADJ
ejpam-2985	143	3	,	,	PUNCT
ejpam-2985	143	4	gx3k+3	gx3k+3	PROPN
ejpam-2985	143	5	)	)	PUNCT
ejpam-2985	143	6	≤	≤	NOUN
ejpam-2985	144	1	3k−1∑	3k−1∑	NUM
ejpam-2985	144	2	i=0	i=0	PUNCT
ejpam-2985	144	3	ϕi	ϕi	X
ejpam-2985	144	4	(	(	PUNCT
ejpam-2985	144	5	d(gx0	d(gx0	PROPN
ejpam-2985	144	6	,	,	PUNCT
ejpam-2985	144	7	gx1	gx1	PROPN
ejpam-2985	144	8	)	)	PUNCT
ejpam-2985	144	9	)	)	PUNCT
ejpam-2985	145	1	+	+	CCONJ
ejpam-2985	145	2	ϕ3k	ϕ3k	PRON
ejpam-2985	145	3	(	(	PUNCT
ejpam-2985	145	4	d(gx0	d(gx0	PROPN
ejpam-2985	145	5	,	,	PUNCT
ejpam-2985	145	6	gx3	gx3	NOUN
ejpam-2985	145	7	)	)	PUNCT
ejpam-2985	145	8	)	)	PUNCT
ejpam-2985	145	9	.	.	PUNCT
ejpam-2985	146	1	(	(	PUNCT
ejpam-2985	146	2	13	13	X
ejpam-2985	146	3	)	)	PUNCT
ejpam-2985	146	4	using	use	VERB
ejpam-2985	146	5	(	(	PUNCT
ejpam-2985	146	6	8)	8)	NUM
ejpam-2985	146	7	and	and	CCONJ
ejpam-2985	146	8	(	(	PUNCT
ejpam-2985	146	9	11	11	NUM
ejpam-2985	146	10	)	)	PUNCT
ejpam-2985	146	11	,	,	PUNCT
ejpam-2985	146	12	for	for	ADP
ejpam-2985	146	13	k	k	PROPN
ejpam-2985	146	14	=	=	SYM
ejpam-2985	146	15	1	1	NUM
ejpam-2985	146	16	,	,	PUNCT
ejpam-2985	146	17	2	2	NUM
ejpam-2985	146	18	,	,	PUNCT
ejpam-2985	146	19	3	3	NUM
ejpam-2985	146	20	,	,	PUNCT
ejpam-2985	146	21	·	·	PUNCT
ejpam-2985	146	22	·	·	PUNCT
ejpam-2985	146	23	·	·	PUNCT
ejpam-2985	146	24	,	,	PUNCT
ejpam-2985	146	25	we	we	PRON
ejpam-2985	146	26	have	have	VERB
ejpam-2985	146	27	d(gxn	d(gxn	NOUN
ejpam-2985	146	28	,	,	PUNCT
ejpam-2985	146	29	gxn+3k+1	gxn+3k+1	NOUN
ejpam-2985	146	30	)	)	PUNCT
ejpam-2985	146	31	≤	≤	NOUN
ejpam-2985	146	32	ϕn	ϕn	ADP
ejpam-2985	146	33	3k∑	3k∑	PROPN
ejpam-2985	146	34	i=0	i=0	PROPN
ejpam-2985	146	35	ϕi	ϕi	X
ejpam-2985	146	36	(	(	PUNCT
ejpam-2985	146	37	d(gx0	d(gx0	PROPN
ejpam-2985	146	38	,	,	PUNCT
ejpam-2985	146	39	gx1	gx1	PROPN
ejpam-2985	146	40	)	)	PUNCT
ejpam-2985	146	41	)	)	PUNCT
ejpam-2985	146	42	≤	≤	NOUN
ejpam-2985	147	1	ϕn	ϕn	X
ejpam-2985	147	2	[	[	PUNCT
ejpam-2985	147	3	3k∑	3k∑	PROPN
ejpam-2985	147	4	i=0	i=0	PROPN
ejpam-2985	147	5	ϕi	ϕi	X
ejpam-2985	147	6	(	(	PUNCT
ejpam-2985	147	7	d(gx0	d(gx0	PROPN
ejpam-2985	147	8	,	,	PUNCT
ejpam-2985	147	9	gx1	gx1	PROPN
ejpam-2985	147	10	)	)	PUNCT
ejpam-2985	147	11	+	+	X
ejpam-2985	148	1	d(gx0	d(gx0	PROPN
ejpam-2985	148	2	,	,	PUNCT
ejpam-2985	148	3	gx2	gx2	PROPN
ejpam-2985	148	4	)	)	PUNCT
ejpam-2985	149	1	+	+	X
ejpam-2985	149	2	d(gx0	d(gx0	ADJ
ejpam-2985	149	3	,	,	PUNCT
ejpam-2985	149	4	gx3	gx3	NOUN
ejpam-2985	149	5	)	)	PUNCT
ejpam-2985	149	6	)	)	PUNCT
ejpam-2985	149	7	]	]	PUNCT
ejpam-2985	150	1	≤	≤	ADV
ejpam-2985	150	2	ϕn	ϕn	X
ejpam-2985	150	3	[	[	PUNCT
ejpam-2985	150	4	∞∑	∞∑	PROPN
ejpam-2985	150	5	i=0	i=0	PROPN
ejpam-2985	150	6	ϕi	ϕi	X
ejpam-2985	150	7	(	(	PUNCT
ejpam-2985	150	8	d(gx0	d(gx0	PROPN
ejpam-2985	150	9	,	,	PUNCT
ejpam-2985	150	10	gx1	gx1	PROPN
ejpam-2985	150	11	)	)	PUNCT
ejpam-2985	150	12	+	+	X
ejpam-2985	150	13	d(gx0	d(gx0	PROPN
ejpam-2985	150	14	,	,	PUNCT
ejpam-2985	150	15	gx2	gx2	PROPN
ejpam-2985	150	16	)	)	PUNCT
ejpam-2985	150	17	+	+	X
ejpam-2985	150	18	d(gx0	d(gx0	ADJ
ejpam-2985	150	19	,	,	PUNCT
ejpam-2985	150	20	gx3	gx3	NOUN
ejpam-2985	150	21	)	)	PUNCT
ejpam-2985	150	22	)	)	PUNCT
ejpam-2985	150	23	]	]	PUNCT
ejpam-2985	150	24	.	.	PUNCT
ejpam-2985	151	1	(	(	PUNCT
ejpam-2985	151	2	14	14	NUM
ejpam-2985	151	3	)	)	PUNCT
ejpam-2985	151	4	similarly	similarly	ADV
ejpam-2985	151	5	for	for	ADP
ejpam-2985	151	6	k	k	PROPN
ejpam-2985	151	7	=	=	SYM
ejpam-2985	151	8	1	1	NUM
ejpam-2985	151	9	,	,	PUNCT
ejpam-2985	151	10	2	2	NUM
ejpam-2985	151	11	,	,	PUNCT
ejpam-2985	151	12	3	3	NUM
ejpam-2985	151	13	,	,	PUNCT
ejpam-2985	151	14	·	·	PUNCT
ejpam-2985	151	15	·	·	PUNCT
ejpam-2985	151	16	·	·	PUNCT
ejpam-2985	151	17	,	,	PUNCT
ejpam-2985	151	18	(	(	PUNCT
ejpam-2985	151	19	9	9	NUM
ejpam-2985	151	20	)	)	PUNCT
ejpam-2985	151	21	and	and	CCONJ
ejpam-2985	151	22	(	(	PUNCT
ejpam-2985	151	23	12	12	NUM
ejpam-2985	151	24	)	)	PUNCT
ejpam-2985	151	25	implies	imply	VERB
ejpam-2985	151	26	that	that	SCONJ
ejpam-2985	151	27	d(gxn	d(gxn	VERB
ejpam-2985	151	28	,	,	PUNCT
ejpam-2985	151	29	gxn+3k+2	gxn+3k+2	NOUN
ejpam-2985	151	30	)	)	PUNCT
ejpam-2985	151	31	≤	≤	NOUN
ejpam-2985	152	1	ϕn	ϕn	ADP
ejpam-2985	152	2	[	[	PUNCT
ejpam-2985	152	3	3k−1∑	3k−1∑	NUM
ejpam-2985	152	4	i=0	i=0	PROPN
ejpam-2985	152	5	ϕi	ϕi	X
ejpam-2985	152	6	(	(	PUNCT
ejpam-2985	152	7	d(gx0	d(gx0	PROPN
ejpam-2985	152	8	,	,	PUNCT
ejpam-2985	152	9	gx1	gx1	PROPN
ejpam-2985	152	10	)	)	PUNCT
ejpam-2985	152	11	)	)	PUNCT
ejpam-2985	153	1	+	+	CCONJ
ejpam-2985	153	2	ϕ3k	ϕ3k	PRON
ejpam-2985	153	3	(	(	PUNCT
ejpam-2985	153	4	d(gx0	d(gx0	PROPN
ejpam-2985	153	5	,	,	PUNCT
ejpam-2985	153	6	gx2	gx2	PROPN
ejpam-2985	153	7	)	)	PUNCT
ejpam-2985	153	8	)	)	PUNCT
ejpam-2985	153	9	]	]	PUNCT
ejpam-2985	154	1	≤	≤	ADV
ejpam-2985	154	2	ϕn	ϕn	X
ejpam-2985	154	3	[	[	PUNCT
ejpam-2985	154	4	∞∑	∞∑	PROPN
ejpam-2985	154	5	i=0	i=0	PROPN
ejpam-2985	154	6	ϕi	ϕi	X
ejpam-2985	154	7	(	(	PUNCT
ejpam-2985	154	8	d(gx0	d(gx0	PROPN
ejpam-2985	154	9	,	,	PUNCT
ejpam-2985	154	10	gx1	gx1	PROPN
ejpam-2985	154	11	)	)	PUNCT
ejpam-2985	154	12	+	+	X
ejpam-2985	154	13	d(gx0	d(gx0	PROPN
ejpam-2985	154	14	,	,	PUNCT
ejpam-2985	154	15	gx2	gx2	PROPN
ejpam-2985	154	16	)	)	PUNCT
ejpam-2985	154	17	+	+	X
ejpam-2985	154	18	d(gx0	d(gx0	ADJ
ejpam-2985	154	19	,	,	PUNCT
ejpam-2985	154	20	gx3	gx3	NOUN
ejpam-2985	154	21	)	)	PUNCT
ejpam-2985	154	22	)	)	PUNCT
ejpam-2985	154	23	]	]	PUNCT
ejpam-2985	154	24	.	.	PUNCT
ejpam-2985	155	1	(	(	PUNCT
ejpam-2985	155	2	15	15	NUM
ejpam-2985	155	3	)	)	PUNCT
ejpam-2985	155	4	again	again	ADV
ejpam-2985	155	5	,	,	PUNCT
ejpam-2985	155	6	for	for	ADP
ejpam-2985	155	7	k	k	PROPN
ejpam-2985	155	8	=	=	SYM
ejpam-2985	155	9	1	1	NUM
ejpam-2985	155	10	,	,	PUNCT
ejpam-2985	155	11	2	2	NUM
ejpam-2985	155	12	,	,	PUNCT
ejpam-2985	155	13	3	3	NUM
ejpam-2985	155	14	,	,	PUNCT
ejpam-2985	155	15	·	·	PUNCT
ejpam-2985	155	16	·	·	PUNCT
ejpam-2985	155	17	·	·	PUNCT
ejpam-2985	155	18	,	,	PUNCT
ejpam-2985	155	19	(	(	PUNCT
ejpam-2985	155	20	10	10	NUM
ejpam-2985	155	21	)	)	PUNCT
ejpam-2985	155	22	and	and	CCONJ
ejpam-2985	155	23	(	(	PUNCT
ejpam-2985	155	24	13	13	NUM
ejpam-2985	155	25	)	)	PUNCT
ejpam-2985	155	26	implies	imply	VERB
ejpam-2985	155	27	that	that	PRON
ejpam-2985	155	28	d(gxn	d(gxn	VERB
ejpam-2985	155	29	,	,	PUNCT
ejpam-2985	155	30	gxn+3k+3	gxn+3k+3	ADJ
ejpam-2985	155	31	)	)	PUNCT
ejpam-2985	155	32	≤	≤	NOUN
ejpam-2985	156	1	ϕn	ϕn	ADP
ejpam-2985	156	2	[	[	PUNCT
ejpam-2985	156	3	∞∑	∞∑	PROPN
ejpam-2985	156	4	i=0	i=0	PROPN
ejpam-2985	156	5	ϕi	ϕi	X
ejpam-2985	156	6	(	(	PUNCT
ejpam-2985	156	7	d(gx0	d(gx0	PROPN
ejpam-2985	156	8	,	,	PUNCT
ejpam-2985	156	9	gx1	gx1	PROPN
ejpam-2985	156	10	)	)	PUNCT
ejpam-2985	156	11	+	+	X
ejpam-2985	156	12	d(gx0	d(gx0	PROPN
ejpam-2985	156	13	,	,	PUNCT
ejpam-2985	156	14	gx2	gx2	PROPN
ejpam-2985	156	15	)	)	PUNCT
ejpam-2985	156	16	+	+	X
ejpam-2985	156	17	d(gx0	d(gx0	ADJ
ejpam-2985	156	18	,	,	PUNCT
ejpam-2985	156	19	gx3	gx3	NOUN
ejpam-2985	156	20	)	)	PUNCT
ejpam-2985	156	21	)	)	PUNCT
ejpam-2985	156	22	]	]	PUNCT
ejpam-2985	156	23	.	.	PUNCT
ejpam-2985	157	1	(	(	PUNCT
ejpam-2985	157	2	16	16	NUM
ejpam-2985	157	3	)	)	PUNCT
ejpam-2985	157	4	a.	a.	NOUN
ejpam-2985	157	5	auwalu	auwalu	PROPN
ejpam-2985	157	6	,	,	PUNCT
ejpam-2985	157	7	e.	e.	PROPN
ejpam-2985	157	8	hınçal	hınçal	PROPN
ejpam-2985	157	9	/	/	SYM
ejpam-2985	157	10	eur	eur	PROPN
ejpam-2985	157	11	.	.	PUNCT
ejpam-2985	158	1	j.	j.	PROPN
ejpam-2985	158	2	pure	pure	PROPN
ejpam-2985	158	3	appl	appl	PROPN
ejpam-2985	158	4	.	.	PROPN
ejpam-2985	158	5	math	math	PROPN
ejpam-2985	158	6	,	,	PUNCT
ejpam-2985	158	7	10	10	NUM
ejpam-2985	158	8	(	(	PUNCT
ejpam-2985	158	9	3	3	NUM
ejpam-2985	158	10	)	)	PUNCT
ejpam-2985	158	11	(	(	PUNCT
ejpam-2985	158	12	2017	2017	NUM
ejpam-2985	158	13	)	)	PUNCT
ejpam-2985	158	14	,	,	PUNCT
ejpam-2985	158	15	473	473	NUM
ejpam-2985	158	16	-	-	SYM
ejpam-2985	158	17	487	487	NUM
ejpam-2985	158	18	479	479	NUM
ejpam-2985	158	19	thus	thus	ADV
ejpam-2985	158	20	,	,	PUNCT
ejpam-2985	158	21	by	by	ADP
ejpam-2985	158	22	(	(	PUNCT
ejpam-2985	158	23	14	14	NUM
ejpam-2985	158	24	)	)	PUNCT
ejpam-2985	158	25	,	,	PUNCT
ejpam-2985	158	26	(	(	PUNCT
ejpam-2985	158	27	15	15	NUM
ejpam-2985	158	28	)	)	PUNCT
ejpam-2985	158	29	,	,	PUNCT
ejpam-2985	158	30	and	and	CCONJ
ejpam-2985	158	31	(	(	PUNCT
ejpam-2985	158	32	16	16	NUM
ejpam-2985	158	33	)	)	PUNCT
ejpam-2985	158	34	,	,	PUNCT
ejpam-2985	158	35	we	we	PRON
ejpam-2985	158	36	have	have	VERB
ejpam-2985	158	37	,	,	PUNCT
ejpam-2985	158	38	for	for	ADP
ejpam-2985	158	39	each	each	DET
ejpam-2985	158	40	m	m	NOUN
ejpam-2985	158	41	,	,	PUNCT
ejpam-2985	158	42	d(gxn	d(gxn	PROPN
ejpam-2985	158	43	,	,	PUNCT
ejpam-2985	158	44	gxn+m	gxn+m	PROPN
ejpam-2985	158	45	)	)	PUNCT
ejpam-2985	158	46	≤	≤	NOUN
ejpam-2985	158	47	ϕn	ϕn	ADP
ejpam-2985	159	1	[	[	PUNCT
ejpam-2985	159	2	∞∑	∞∑	PROPN
ejpam-2985	159	3	i=0	i=0	PROPN
ejpam-2985	159	4	ϕi	ϕi	X
ejpam-2985	159	5	(	(	PUNCT
ejpam-2985	159	6	d(gx0	d(gx0	PROPN
ejpam-2985	159	7	,	,	PUNCT
ejpam-2985	159	8	gx1	gx1	PROPN
ejpam-2985	159	9	)	)	PUNCT
ejpam-2985	160	1	+	+	X
ejpam-2985	160	2	d(gx0	d(gx0	PROPN
ejpam-2985	160	3	,	,	PUNCT
ejpam-2985	160	4	gx2	gx2	PROPN
ejpam-2985	160	5	)	)	PUNCT
ejpam-2985	161	1	+	+	X
ejpam-2985	161	2	d(gx0	d(gx0	ADJ
ejpam-2985	161	3	,	,	PUNCT
ejpam-2985	161	4	gx3	gx3	NOUN
ejpam-2985	161	5	)	)	PUNCT
ejpam-2985	161	6	)	)	PUNCT
ejpam-2985	161	7	]	]	PUNCT
ejpam-2985	161	8	.	.	PUNCT
ejpam-2985	162	1	(	(	PUNCT
ejpam-2985	162	2	17	17	NUM
ejpam-2985	162	3	)	)	PUNCT
ejpam-2985	162	4	since	since	SCONJ
ejpam-2985	162	5	∑∞	∑∞	VERB
ejpam-2985	162	6	i=0	i=0	PROPN
ejpam-2985	162	7	ϕ	ϕ	X
ejpam-2985	162	8	i	i	PRON
ejpam-2985	162	9	(	(	PUNCT
ejpam-2985	162	10	d(gx0	d(gx0	PROPN
ejpam-2985	162	11	,	,	PUNCT
ejpam-2985	162	12	gx1	gx1	PROPN
ejpam-2985	162	13	)	)	PUNCT
ejpam-2985	163	1	+	+	X
ejpam-2985	163	2	d(gx0	d(gx0	PROPN
ejpam-2985	163	3	,	,	PUNCT
ejpam-2985	163	4	gx2	gx2	PROPN
ejpam-2985	163	5	)	)	PUNCT
ejpam-2985	164	1	+	+	X
ejpam-2985	164	2	d(gx0	d(gx0	ADJ
ejpam-2985	164	3	,	,	PUNCT
ejpam-2985	164	4	gx3	gx3	NOUN
ejpam-2985	164	5	)	)	PUNCT
ejpam-2985	164	6	)	)	PUNCT
ejpam-2985	165	1	converges	converge	VERB
ejpam-2985	165	2	(	(	PUNCT
ejpam-2985	165	3	by	by	ADP
ejpam-2985	165	4	definition	definition	NOUN
ejpam-2985	165	5	5	5	NUM
ejpam-2985	165	6	)	)	PUNCT
ejpam-2985	165	7	,	,	PUNCT
ejpam-2985	165	8	where	where	SCONJ
ejpam-2985	165	9	d(gx0	d(gx0	ADJ
ejpam-2985	165	10	,	,	PUNCT
ejpam-2985	165	11	gx1)+d(gx0	gx1)+d(gx0	PROPN
ejpam-2985	165	12	,	,	PUNCT
ejpam-2985	165	13	gx2)+d(gx0	gx2)+d(gx0	PROPN
ejpam-2985	165	14	,	,	PUNCT
ejpam-2985	165	15	gx3	gx3	NOUN
ejpam-2985	165	16	)	)	PUNCT
ejpam-2985	165	17	∈	∈	PROPN
ejpam-2985	165	18	p\{0	p\{0	PROPN
ejpam-2985	165	19	}	}	PUNCT
ejpam-2985	165	20	,	,	PUNCT
ejpam-2985	165	21	and	and	CCONJ
ejpam-2985	165	22	p	p	NOUN
ejpam-2985	165	23	is	be	AUX
ejpam-2985	165	24	closed	closed	ADJ
ejpam-2985	165	25	,	,	PUNCT
ejpam-2985	165	26	then	then	ADV
ejpam-2985	165	27	∑∞	∑∞	X
ejpam-2985	166	1	i=0	i=0	PROPN
ejpam-2985	166	2	ϕ	ϕ	X
ejpam-2985	166	3	i	i	PRON
ejpam-2985	166	4	(	(	PUNCT
ejpam-2985	166	5	d(gx0	d(gx0	PROPN
ejpam-2985	166	6	,	,	PUNCT
ejpam-2985	166	7	gx1)+	gx1)+	PROPN
ejpam-2985	166	8	d(gx0	d(gx0	PROPN
ejpam-2985	166	9	,	,	PUNCT
ejpam-2985	166	10	gx2	gx2	PROPN
ejpam-2985	166	11	)	)	PUNCT
ejpam-2985	166	12	+	+	X
ejpam-2985	166	13	d(gx0	d(gx0	ADJ
ejpam-2985	166	14	,	,	PUNCT
ejpam-2985	166	15	gx3	gx3	NOUN
ejpam-2985	166	16	)	)	PUNCT
ejpam-2985	166	17	)	)	PUNCT
ejpam-2985	166	18	∈	∈	PROPN
ejpam-2985	167	1	p	p	NOUN
ejpam-2985	167	2	\	\	PROPN
ejpam-2985	167	3	{	{	PUNCT
ejpam-2985	167	4	0	0	NUM
ejpam-2985	167	5	}	}	PUNCT
ejpam-2985	167	6	.	.	PUNCT
ejpam-2985	168	1	hence	hence	ADV
ejpam-2985	168	2	lim	lim	PROPN
ejpam-2985	168	3	n→∞	n→∞	PROPN
ejpam-2985	169	1	ϕn	ϕn	X
ejpam-2985	169	2	[	[	PUNCT
ejpam-2985	169	3	∞∑	∞∑	PROPN
ejpam-2985	169	4	i=0	i=0	PROPN
ejpam-2985	169	5	ϕi	ϕi	X
ejpam-2985	169	6	(	(	PUNCT
ejpam-2985	169	7	d(gx0	d(gx0	PROPN
ejpam-2985	169	8	,	,	PUNCT
ejpam-2985	169	9	gx1	gx1	PROPN
ejpam-2985	169	10	)	)	PUNCT
ejpam-2985	169	11	+	+	X
ejpam-2985	170	1	d(gx0	d(gx0	PROPN
ejpam-2985	170	2	,	,	PUNCT
ejpam-2985	170	3	gx2	gx2	PROPN
ejpam-2985	170	4	)	)	PUNCT
ejpam-2985	171	1	+	+	X
ejpam-2985	171	2	d(gx0	d(gx0	ADJ
ejpam-2985	171	3	,	,	PUNCT
ejpam-2985	171	4	gx3	gx3	NOUN
ejpam-2985	171	5	)	)	PUNCT
ejpam-2985	171	6	)	)	PUNCT
ejpam-2985	171	7	]	]	PUNCT
ejpam-2985	172	1	=	=	PUNCT
ejpam-2985	172	2	0	0	X
ejpam-2985	172	3	.	.	PUNCT
ejpam-2985	173	1	then	then	ADV
ejpam-2985	173	2	,	,	PUNCT
ejpam-2985	173	3	for	for	ADP
ejpam-2985	173	4	given	give	VERB
ejpam-2985	173	5	c	c	PROPN
ejpam-2985	173	6	�	�	PROPN
ejpam-2985	173	7	0	0	NUM
ejpam-2985	173	8	,	,	PUNCT
ejpam-2985	173	9	there	there	PRON
ejpam-2985	173	10	is	be	VERB
ejpam-2985	173	11	a	a	DET
ejpam-2985	173	12	natural	natural	ADJ
ejpam-2985	173	13	number	number	NOUN
ejpam-2985	173	14	n1	n1	NOUN
ejpam-2985	173	15	such	such	ADJ
ejpam-2985	173	16	that	that	SCONJ
ejpam-2985	173	17	ϕn	ϕn	PROPN
ejpam-2985	174	1	[	[	PUNCT
ejpam-2985	174	2	∞∑	∞∑	PROPN
ejpam-2985	174	3	i=0	i=0	PROPN
ejpam-2985	174	4	ϕi	ϕi	X
ejpam-2985	174	5	(	(	PUNCT
ejpam-2985	174	6	d(gx0	d(gx0	PROPN
ejpam-2985	174	7	,	,	PUNCT
ejpam-2985	174	8	gx1	gx1	PROPN
ejpam-2985	174	9	)	)	PUNCT
ejpam-2985	175	1	+	+	X
ejpam-2985	175	2	d(gx0	d(gx0	PROPN
ejpam-2985	175	3	,	,	PUNCT
ejpam-2985	175	4	gx2	gx2	PROPN
ejpam-2985	175	5	)	)	PUNCT
ejpam-2985	176	1	+	+	X
ejpam-2985	176	2	d(gx0	d(gx0	ADJ
ejpam-2985	176	3	,	,	PUNCT
ejpam-2985	176	4	gx3	gx3	NOUN
ejpam-2985	176	5	)	)	PUNCT
ejpam-2985	176	6	)	)	PUNCT
ejpam-2985	176	7	]	]	PUNCT
ejpam-2985	177	1	�	�	PROPN
ejpam-2985	177	2	c	c	PROPN
ejpam-2985	177	3	,	,	PUNCT
ejpam-2985	177	4	∀n	∀n	NUM
ejpam-2985	177	5	≥	≥	NOUN
ejpam-2985	177	6	n1	n1	NOUN
ejpam-2985	177	7	.	.	PUNCT
ejpam-2985	177	8	(	(	PUNCT
ejpam-2985	177	9	18	18	NUM
ejpam-2985	177	10	)	)	PUNCT
ejpam-2985	177	11	thus	thus	ADV
ejpam-2985	177	12	,	,	PUNCT
ejpam-2985	177	13	from	from	ADP
ejpam-2985	177	14	(	(	PUNCT
ejpam-2985	177	15	17	17	NUM
ejpam-2985	177	16	)	)	PUNCT
ejpam-2985	177	17	and	and	CCONJ
ejpam-2985	177	18	(	(	PUNCT
ejpam-2985	177	19	18	18	NUM
ejpam-2985	177	20	)	)	PUNCT
ejpam-2985	177	21	,	,	PUNCT
ejpam-2985	177	22	we	we	PRON
ejpam-2985	177	23	have	have	VERB
ejpam-2985	177	24	d(gxn	d(gxn	NOUN
ejpam-2985	177	25	,	,	PUNCT
ejpam-2985	177	26	gxn+m	gxn+m	PROPN
ejpam-2985	177	27	)	)	PUNCT
ejpam-2985	177	28	�	�	PROPN
ejpam-2985	177	29	c	c	NOUN
ejpam-2985	177	30	,	,	PUNCT
ejpam-2985	177	31	for	for	ADP
ejpam-2985	177	32	all	all	DET
ejpam-2985	177	33	n	n	PRON
ejpam-2985	177	34	≥	≥	NOUN
ejpam-2985	177	35	n1	n1	NOUN
ejpam-2985	177	36	.	.	PUNCT
ejpam-2985	178	1	therefore	therefore	ADV
ejpam-2985	178	2	,	,	PUNCT
ejpam-2985	178	3	{	{	PUNCT
ejpam-2985	178	4	gxn	gxn	INTJ
ejpam-2985	178	5	}	}	PUNCT
ejpam-2985	178	6	is	be	AUX
ejpam-2985	178	7	a	a	DET
ejpam-2985	178	8	cauchy	cauchy	ADJ
ejpam-2985	178	9	sequence	sequence	NOUN
ejpam-2985	178	10	in	in	ADP
ejpam-2985	178	11	x.	x.	NOUN
ejpam-2985	178	12	since	since	SCONJ
ejpam-2985	178	13	g(x	g(x	NOUN
ejpam-2985	178	14	)	)	PUNCT
ejpam-2985	178	15	is	be	AUX
ejpam-2985	178	16	a	a	DET
ejpam-2985	178	17	complete	complete	ADJ
ejpam-2985	178	18	subspace	subspace	NOUN
ejpam-2985	178	19	of	of	ADP
ejpam-2985	178	20	x	x	PRON
ejpam-2985	178	21	,	,	PUNCT
ejpam-2985	178	22	there	there	PRON
ejpam-2985	178	23	exists	exist	VERB
ejpam-2985	178	24	a	a	DET
ejpam-2985	178	25	points	point	NOUN
ejpam-2985	178	26	u	u	NOUN
ejpam-2985	178	27	,	,	PUNCT
ejpam-2985	178	28	v	v	NOUN
ejpam-2985	178	29	∈	∈	PROPN
ejpam-2985	178	30	g(x	g(x	NOUN
ejpam-2985	178	31	)	)	PUNCT
ejpam-2985	178	32	such	such	ADJ
ejpam-2985	178	33	that	that	SCONJ
ejpam-2985	178	34	limn→∞	limn→∞	PROPN
ejpam-2985	178	35	gxn	gxn	NOUN
ejpam-2985	178	36	=	=	SYM
ejpam-2985	178	37	v	v	NOUN
ejpam-2985	178	38	=	=	SYM
ejpam-2985	178	39	gu	gu	NOUN
ejpam-2985	178	40	.	.	PUNCT
ejpam-2985	179	1	now	now	ADV
ejpam-2985	179	2	,	,	PUNCT
ejpam-2985	179	3	we	we	PRON
ejpam-2985	179	4	show	show	VERB
ejpam-2985	179	5	that	that	SCONJ
ejpam-2985	179	6	gu	gu	NOUN
ejpam-2985	179	7	=	=	SYM
ejpam-2985	179	8	su	su	PROPN
ejpam-2985	179	9	.	.	PROPN
ejpam-2985	179	10	given	give	VERB
ejpam-2985	179	11	c	c	PROPN
ejpam-2985	179	12	�	�	PROPN
ejpam-2985	179	13	0	0	NUM
ejpam-2985	179	14	,	,	PUNCT
ejpam-2985	179	15	we	we	PRON
ejpam-2985	179	16	choose	choose	VERB
ejpam-2985	179	17	a	a	DET
ejpam-2985	179	18	natural	natural	ADJ
ejpam-2985	179	19	numbers	number	NOUN
ejpam-2985	179	20	n2	n2	ADJ
ejpam-2985	179	21	,	,	PUNCT
ejpam-2985	179	22	n3	n3	NOUN
ejpam-2985	179	23	such	such	ADJ
ejpam-2985	179	24	that	that	SCONJ
ejpam-2985	179	25	d(v	d(v	PROPN
ejpam-2985	179	26	,	,	PUNCT
ejpam-2985	179	27	gxn	gxn	ADJ
ejpam-2985	179	28	)	)	PUNCT
ejpam-2985	179	29	�	�	PROPN
ejpam-2985	180	1	c	c	PROPN
ejpam-2985	180	2	4	4	NUM
ejpam-2985	180	3	,	,	PUNCT
ejpam-2985	180	4	∀n	∀n	NUM
ejpam-2985	180	5	≥	≥	NOUN
ejpam-2985	180	6	n2	n2	NOUN
ejpam-2985	180	7	,	,	PUNCT
ejpam-2985	180	8	and	and	CCONJ
ejpam-2985	180	9	d(gxn	d(gxn	VERB
ejpam-2985	180	10	,	,	PUNCT
ejpam-2985	180	11	gxn+1	gxn+1	PROPN
ejpam-2985	180	12	)	)	PUNCT
ejpam-2985	180	13	�	�	PROPN
ejpam-2985	180	14	c	c	PROPN
ejpam-2985	180	15	4	4	NUM
ejpam-2985	180	16	,	,	PUNCT
ejpam-2985	180	17	∀n	∀n	NUM
ejpam-2985	180	18	≥	≥	NOUN
ejpam-2985	180	19	n3	n3	VERB
ejpam-2985	180	20	.	.	PUNCT
ejpam-2985	181	1	since	since	SCONJ
ejpam-2985	181	2	xn	xn	PROPN
ejpam-2985	181	3	6=	6=	NUM
ejpam-2985	181	4	xm	xm	PROPN
ejpam-2985	181	5	for	for	ADP
ejpam-2985	181	6	n	n	PROPN
ejpam-2985	181	7	6=	6=	NUM
ejpam-2985	181	8	m	m	PROPN
ejpam-2985	181	9	,	,	PUNCT
ejpam-2985	181	10	by	by	ADP
ejpam-2985	181	11	pentagonal	pentagonal	ADJ
ejpam-2985	181	12	property	property	NOUN
ejpam-2985	181	13	,	,	PUNCT
ejpam-2985	181	14	we	we	PRON
ejpam-2985	181	15	have	have	VERB
ejpam-2985	181	16	that	that	DET
ejpam-2985	181	17	d(gu	d(gu	PROPN
ejpam-2985	181	18	,	,	PUNCT
ejpam-2985	181	19	su	su	NOUN
ejpam-2985	181	20	)	)	PUNCT
ejpam-2985	181	21	≤	≤	NOUN
ejpam-2985	181	22	d(gu	d(gu	PROPN
ejpam-2985	181	23	,	,	PUNCT
ejpam-2985	181	24	gxn	gxn	PROPN
ejpam-2985	181	25	)	)	PUNCT
ejpam-2985	181	26	+	+	CCONJ
ejpam-2985	181	27	d(gxn	d(gxn	PROPN
ejpam-2985	181	28	,	,	PUNCT
ejpam-2985	181	29	gxn+1	gxn+1	NOUN
ejpam-2985	181	30	)	)	PUNCT
ejpam-2985	182	1	+	+	CCONJ
ejpam-2985	182	2	d(gxn+1	d(gxn+1	NOUN
ejpam-2985	182	3	,	,	PUNCT
ejpam-2985	182	4	gxn+2	gxn+2	PROPN
ejpam-2985	182	5	)	)	PUNCT
ejpam-2985	183	1	+	+	CCONJ
ejpam-2985	183	2	d(gxn+2	d(gxn+2	PROPN
ejpam-2985	183	3	,	,	PUNCT
ejpam-2985	183	4	su	su	NOUN
ejpam-2985	183	5	)	)	PUNCT
ejpam-2985	184	1	=	=	SYM
ejpam-2985	184	2	d(v	d(v	ADJ
ejpam-2985	184	3	,	,	PUNCT
ejpam-2985	184	4	gxn	gxn	ADJ
ejpam-2985	184	5	)	)	PUNCT
ejpam-2985	184	6	+	+	CCONJ
ejpam-2985	184	7	d(gxn	d(gxn	PROPN
ejpam-2985	184	8	,	,	PUNCT
ejpam-2985	184	9	gxn+1	gxn+1	NOUN
ejpam-2985	184	10	)	)	PUNCT
ejpam-2985	185	1	+	+	CCONJ
ejpam-2985	185	2	d(gxn+1	d(gxn+1	NOUN
ejpam-2985	185	3	,	,	PUNCT
ejpam-2985	185	4	gxn+2	gxn+2	PROPN
ejpam-2985	185	5	)	)	PUNCT
ejpam-2985	186	1	+	+	PUNCT
ejpam-2985	186	2	d(su	d(su	ADJ
ejpam-2985	186	3	,	,	PUNCT
ejpam-2985	186	4	fxn+1	fxn+1	NOUN
ejpam-2985	186	5	)	)	PUNCT
ejpam-2985	186	6	≤	≤	NOUN
ejpam-2985	187	1	d(v	d(v	PROPN
ejpam-2985	187	2	,	,	PUNCT
ejpam-2985	187	3	gxn	gxn	ADJ
ejpam-2985	187	4	)	)	PUNCT
ejpam-2985	187	5	+	+	CCONJ
ejpam-2985	187	6	d(gxn	d(gxn	PROPN
ejpam-2985	187	7	,	,	PUNCT
ejpam-2985	187	8	gxn+1	gxn+1	NOUN
ejpam-2985	187	9	)	)	PUNCT
ejpam-2985	187	10	+	+	CCONJ
ejpam-2985	187	11	d(gxn+1	d(gxn+1	NOUN
ejpam-2985	187	12	,	,	PUNCT
ejpam-2985	187	13	gxn+2	gxn+2	PROPN
ejpam-2985	187	14	)	)	PUNCT
ejpam-2985	188	1	+	+	PUNCT
ejpam-2985	188	2	ϕ	ϕ	X
ejpam-2985	188	3	(	(	PUNCT
ejpam-2985	188	4	d(gu	d(gu	PROPN
ejpam-2985	188	5	,	,	PUNCT
ejpam-2985	188	6	gxn+1	gxn+1	PROPN
ejpam-2985	188	7	)	)	PUNCT
ejpam-2985	188	8	)	)	PUNCT
ejpam-2985	189	1	<	<	X
ejpam-2985	189	2	d(v	d(v	PROPN
ejpam-2985	189	3	,	,	PUNCT
ejpam-2985	189	4	gxn	gxn	ADJ
ejpam-2985	189	5	)	)	PUNCT
ejpam-2985	189	6	+	+	CCONJ
ejpam-2985	189	7	d(gxn	d(gxn	PROPN
ejpam-2985	189	8	,	,	PUNCT
ejpam-2985	189	9	gxn+1	gxn+1	NOUN
ejpam-2985	189	10	)	)	PUNCT
ejpam-2985	189	11	+	+	CCONJ
ejpam-2985	189	12	d(gxn+1	d(gxn+1	NOUN
ejpam-2985	189	13	,	,	PUNCT
ejpam-2985	189	14	gxn+2	gxn+2	PROPN
ejpam-2985	189	15	)	)	PUNCT
ejpam-2985	190	1	+	+	X
ejpam-2985	190	2	d(v	d(v	PROPN
ejpam-2985	190	3	,	,	PUNCT
ejpam-2985	190	4	gxn+1	gxn+1	PROPN
ejpam-2985	190	5	)	)	PUNCT
ejpam-2985	190	6	�	�	PROPN
ejpam-2985	190	7	c	c	NOUN
ejpam-2985	190	8	4	4	NUM
ejpam-2985	191	1	+	+	SYM
ejpam-2985	191	2	c	c	NOUN
ejpam-2985	191	3	4	4	NUM
ejpam-2985	191	4	+	+	SYM
ejpam-2985	191	5	c	c	NOUN
ejpam-2985	191	6	4	4	NUM
ejpam-2985	191	7	+	+	SYM
ejpam-2985	191	8	c	c	NOUN
ejpam-2985	191	9	4	4	NUM
ejpam-2985	191	10	=	=	SYM
ejpam-2985	191	11	c	c	NOUN
ejpam-2985	191	12	,	,	PUNCT
ejpam-2985	191	13	for	for	ADP
ejpam-2985	191	14	all	all	DET
ejpam-2985	191	15	n	n	DET
ejpam-2985	191	16	≥	≥	NOUN
ejpam-2985	191	17	n	n	CCONJ
ejpam-2985	191	18	,	,	PUNCT
ejpam-2985	191	19	where	where	SCONJ
ejpam-2985	191	20	n	n	X
ejpam-2985	191	21	:	:	PUNCT
ejpam-2985	191	22	=	=	NOUN
ejpam-2985	191	23	max{n2	max{n2	NOUN
ejpam-2985	191	24	,	,	PUNCT
ejpam-2985	191	25	n3	n3	NOUN
ejpam-2985	191	26	}	}	PUNCT
ejpam-2985	191	27	.	.	PUNCT
ejpam-2985	192	1	since	since	SCONJ
ejpam-2985	192	2	c	c	PROPN
ejpam-2985	192	3	is	be	AUX
ejpam-2985	192	4	arbitrary	arbitrary	ADJ
ejpam-2985	192	5	,	,	PUNCT
ejpam-2985	192	6	we	we	PRON
ejpam-2985	192	7	have	have	VERB
ejpam-2985	192	8	d(gu	d(gu	PROPN
ejpam-2985	192	9	,	,	PUNCT
ejpam-2985	192	10	su	su	PROPN
ejpam-2985	192	11	)	)	PUNCT
ejpam-2985	192	12	�	�	PROPN
ejpam-2985	192	13	c	c	NOUN
ejpam-2985	192	14	m	m	PROPN
ejpam-2985	192	15	,	,	PUNCT
ejpam-2985	192	16	∀m	∀m	PROPN
ejpam-2985	192	17	∈	∈	PROPN
ejpam-2985	192	18	n.	n.	NOUN
ejpam-2985	192	19	since	since	SCONJ
ejpam-2985	192	20	c	c	PROPN
ejpam-2985	192	21	m	m	PROPN
ejpam-2985	192	22	→	→	SYM
ejpam-2985	192	23	0	0	NUM
ejpam-2985	193	1	as	as	SCONJ
ejpam-2985	193	2	m	m	PROPN
ejpam-2985	193	3	→	→	SYM
ejpam-2985	193	4	∞	∞	PROPN
ejpam-2985	193	5	,	,	PUNCT
ejpam-2985	193	6	we	we	PRON
ejpam-2985	193	7	conclude	conclude	VERB
ejpam-2985	193	8	c	c	PROPN
ejpam-2985	193	9	m	m	VERB
ejpam-2985	193	10	−	−	PROPN
ejpam-2985	193	11	d(gu	d(gu	PROPN
ejpam-2985	193	12	,	,	PUNCT
ejpam-2985	193	13	su	su	NOUN
ejpam-2985	193	14	)	)	PUNCT
ejpam-2985	193	15	→	→	SYM
ejpam-2985	193	16	−d(gu	−d(gu	PROPN
ejpam-2985	193	17	,	,	PUNCT
ejpam-2985	193	18	su	su	PROPN
ejpam-2985	193	19	)	)	PUNCT
ejpam-2985	193	20	as	as	ADP
ejpam-2985	193	21	m	m	PROPN
ejpam-2985	193	22	→	→	SYM
ejpam-2985	193	23	∞.	∞.	PROPN
ejpam-2985	193	24	since	since	SCONJ
ejpam-2985	193	25	p	p	NOUN
ejpam-2985	193	26	is	be	AUX
ejpam-2985	193	27	closed	closed	ADJ
ejpam-2985	193	28	,	,	PUNCT
ejpam-2985	194	1	−d(gu	−d(gu	NOUN
ejpam-2985	194	2	,	,	PUNCT
ejpam-2985	194	3	su	su	PROPN
ejpam-2985	194	4	)	)	PUNCT
ejpam-2985	194	5	∈	∈	PROPN
ejpam-2985	194	6	p.	p.	NOUN
ejpam-2985	194	7	hence	hence	ADV
ejpam-2985	194	8	d(gu	d(gu	PROPN
ejpam-2985	194	9	,	,	PUNCT
ejpam-2985	194	10	su	su	NOUN
ejpam-2985	194	11	)	)	PUNCT
ejpam-2985	194	12	∈	∈	PROPN
ejpam-2985	194	13	p	p	NOUN
ejpam-2985	194	14	∩	∩	ADJ
ejpam-2985	194	15	−p	−p	NOUN
ejpam-2985	194	16	.	.	PUNCT
ejpam-2985	195	1	by	by	ADP
ejpam-2985	195	2	definition	definition	NOUN
ejpam-2985	195	3	of	of	ADP
ejpam-2985	195	4	cone	cone	NOUN
ejpam-2985	195	5	we	we	PRON
ejpam-2985	195	6	get	get	VERB
ejpam-2985	195	7	that	that	DET
ejpam-2985	195	8	d(gu	d(gu	PROPN
ejpam-2985	195	9	,	,	PUNCT
ejpam-2985	195	10	su	su	NOUN
ejpam-2985	195	11	)	)	PUNCT
ejpam-2985	195	12	=	=	SYM
ejpam-2985	195	13	0	0	NUM
ejpam-2985	195	14	,	,	PUNCT
ejpam-2985	195	15	and	and	CCONJ
ejpam-2985	195	16	so	so	ADV
ejpam-2985	195	17	gu	gu	NOUN
ejpam-2985	195	18	=	=	SYM
ejpam-2985	195	19	su	su	PROPN
ejpam-2985	196	1	=	=	NOUN
ejpam-2985	196	2	v.	v.	ADP
ejpam-2985	196	3	hence	hence	ADV
ejpam-2985	196	4	,	,	PUNCT
ejpam-2985	196	5	v	v	PRON
ejpam-2985	196	6	is	be	AUX
ejpam-2985	196	7	a	a	DET
ejpam-2985	196	8	coincidence	coincidence	NOUN
ejpam-2985	196	9	point	point	NOUN
ejpam-2985	196	10	of	of	ADP
ejpam-2985	196	11	s	s	PRON
ejpam-2985	196	12	and	and	CCONJ
ejpam-2985	196	13	g.	g.	PROPN
ejpam-2985	196	14	similarly	similarly	ADV
ejpam-2985	196	15	,	,	PUNCT
ejpam-2985	196	16	we	we	PRON
ejpam-2985	196	17	can	can	AUX
ejpam-2985	196	18	prove	prove	VERB
ejpam-2985	196	19	that	that	DET
ejpam-2985	196	20	gu	gu	NOUN
ejpam-2985	196	21	=	=	PUNCT
ejpam-2985	196	22	fu	fu	NOUN
ejpam-2985	196	23	=	=	SYM
ejpam-2985	196	24	v	v	NOUN
ejpam-2985	196	25	,	,	PUNCT
ejpam-2985	196	26	which	which	PRON
ejpam-2985	196	27	implies	imply	VERB
ejpam-2985	196	28	that	that	SCONJ
ejpam-2985	196	29	v	v	NOUN
ejpam-2985	196	30	is	be	AUX
ejpam-2985	196	31	a	a	DET
ejpam-2985	196	32	point	point	NOUN
ejpam-2985	196	33	of	of	ADP
ejpam-2985	196	34	coincidence	coincidence	NOUN
ejpam-2985	196	35	of	of	ADP
ejpam-2985	196	36	s	s	PROPN
ejpam-2985	196	37	,	,	PUNCT
ejpam-2985	196	38	f	f	PROPN
ejpam-2985	196	39	and	and	CCONJ
ejpam-2985	196	40	g	g	PROPN
ejpam-2985	196	41	,	,	PUNCT
ejpam-2985	196	42	i.e.	i.e.	X
ejpam-2985	196	43	gu	gu	X
ejpam-2985	196	44	=	=	PUNCT
ejpam-2985	196	45	fu	fu	NOUN
ejpam-2985	196	46	=	=	PUNCT
ejpam-2985	196	47	su	su	PROPN
ejpam-2985	197	1	=	=	PROPN
ejpam-2985	197	2	v.	v.	ADP
ejpam-2985	197	3	next	next	ADV
ejpam-2985	197	4	,	,	PUNCT
ejpam-2985	197	5	we	we	PRON
ejpam-2985	197	6	show	show	VERB
ejpam-2985	197	7	that	that	SCONJ
ejpam-2985	197	8	v	v	NOUN
ejpam-2985	197	9	is	be	AUX
ejpam-2985	197	10	unique	unique	ADJ
ejpam-2985	197	11	.	.	PUNCT
ejpam-2985	198	1	for	for	ADP
ejpam-2985	198	2	suppose	suppose	VERB
ejpam-2985	198	3	v′	v′	NOUN
ejpam-2985	198	4	be	be	AUX
ejpam-2985	198	5	another	another	DET
ejpam-2985	198	6	point	point	NOUN
ejpam-2985	198	7	of	of	ADP
ejpam-2985	198	8	coincidence	coincidence	NOUN
ejpam-2985	198	9	of	of	ADP
ejpam-2985	198	10	s	s	PROPN
ejpam-2985	198	11	,	,	PUNCT
ejpam-2985	198	12	f	f	PROPN
ejpam-2985	198	13	and	and	CCONJ
ejpam-2985	198	14	g	g	PROPN
ejpam-2985	198	15	,	,	PUNCT
ejpam-2985	198	16	that	that	PRON
ejpam-2985	198	17	is	be	AUX
ejpam-2985	198	18	su′	su′	ADJ
ejpam-2985	198	19	=	=	SYM
ejpam-2985	198	20	fu′	fu′	NOUN
ejpam-2985	198	21	=	=	SYM
ejpam-2985	198	22	gu′	gu′	NOUN
ejpam-2985	198	23	=	=	SYM
ejpam-2985	198	24	v′	v′	NOUN
ejpam-2985	198	25	,	,	PUNCT
ejpam-2985	198	26	for	for	ADP
ejpam-2985	198	27	some	some	DET
ejpam-2985	198	28	u′	u′	PROPN
ejpam-2985	198	29	∈	∈	PROPN
ejpam-2985	198	30	x	x	NOUN
ejpam-2985	198	31	,	,	PUNCT
ejpam-2985	198	32	then	then	ADV
ejpam-2985	198	33	d(v	d(v	PROPN
ejpam-2985	198	34	,	,	PUNCT
ejpam-2985	198	35	v′	v′	NOUN
ejpam-2985	198	36	)	)	PUNCT
ejpam-2985	198	37	=	=	PUNCT
ejpam-2985	198	38	d(su	d(su	ADJ
ejpam-2985	198	39	,	,	PUNCT
ejpam-2985	198	40	fu′	fu′	NOUN
ejpam-2985	198	41	)	)	PUNCT
ejpam-2985	198	42	≤	≤	NOUN
ejpam-2985	198	43	ϕ	ϕ	X
ejpam-2985	198	44	(	(	PUNCT
ejpam-2985	198	45	d(gu	d(gu	PROPN
ejpam-2985	198	46	,	,	PUNCT
ejpam-2985	198	47	gu′	gu′	NOUN
ejpam-2985	198	48	)	)	PUNCT
ejpam-2985	198	49	)	)	PUNCT
ejpam-2985	199	1	=	=	SYM
ejpam-2985	199	2	ϕ	ϕ	PROPN
ejpam-2985	199	3	(	(	PUNCT
ejpam-2985	199	4	d(v	d(v	PROPN
ejpam-2985	199	5	,	,	PUNCT
ejpam-2985	199	6	v′	v′	NOUN
ejpam-2985	199	7	)	)	PUNCT
ejpam-2985	199	8	)	)	PUNCT
ejpam-2985	200	1	<	<	X
ejpam-2985	200	2	d(v	d(v	PROPN
ejpam-2985	200	3	,	,	PUNCT
ejpam-2985	200	4	v′	v′	NUM
ejpam-2985	200	5	)	)	PUNCT
ejpam-2985	200	6	.	.	PUNCT
ejpam-2985	201	1	a.	a.	PROPN
ejpam-2985	201	2	auwalu	auwalu	PROPN
ejpam-2985	201	3	,	,	PUNCT
ejpam-2985	201	4	e.	e.	PROPN
ejpam-2985	201	5	hınçal	hınçal	PROPN
ejpam-2985	201	6	/	/	SYM
ejpam-2985	201	7	eur	eur	PROPN
ejpam-2985	201	8	.	.	PUNCT
ejpam-2985	202	1	j.	j.	PROPN
ejpam-2985	202	2	pure	pure	PROPN
ejpam-2985	202	3	appl	appl	PROPN
ejpam-2985	202	4	.	.	PROPN
ejpam-2985	202	5	math	math	PROPN
ejpam-2985	202	6	,	,	PUNCT
ejpam-2985	202	7	10	10	NUM
ejpam-2985	202	8	(	(	PUNCT
ejpam-2985	202	9	3	3	NUM
ejpam-2985	202	10	)	)	PUNCT
ejpam-2985	202	11	(	(	PUNCT
ejpam-2985	202	12	2017	2017	NUM
ejpam-2985	202	13	)	)	PUNCT
ejpam-2985	202	14	,	,	PUNCT
ejpam-2985	202	15	473	473	NUM
ejpam-2985	202	16	-	-	SYM
ejpam-2985	202	17	487	487	NUM
ejpam-2985	202	18	480	480	NUM
ejpam-2985	202	19	hence	hence	ADV
ejpam-2985	202	20	v	v	ADJ
ejpam-2985	202	21	=	=	SYM
ejpam-2985	202	22	v′.	v′.	INTJ
ejpam-2985	202	23	since	since	SCONJ
ejpam-2985	202	24	(	(	PUNCT
ejpam-2985	202	25	s	s	X
ejpam-2985	202	26	,	,	PUNCT
ejpam-2985	202	27	g	g	NOUN
ejpam-2985	202	28	)	)	PUNCT
ejpam-2985	202	29	and	and	CCONJ
ejpam-2985	202	30	(	(	PUNCT
ejpam-2985	202	31	f	f	X
ejpam-2985	202	32	,	,	PUNCT
ejpam-2985	202	33	g	g	NOUN
ejpam-2985	202	34	)	)	PUNCT
ejpam-2985	202	35	are	be	AUX
ejpam-2985	202	36	weakly	weakly	ADV
ejpam-2985	202	37	compatible	compatible	ADJ
ejpam-2985	202	38	,	,	PUNCT
ejpam-2985	202	39	by	by	ADP
ejpam-2985	202	40	lemma	lemma	PROPN
ejpam-2985	202	41	1	1	NUM
ejpam-2985	202	42	,	,	PUNCT
ejpam-2985	202	43	v	v	NOUN
ejpam-2985	202	44	is	be	AUX
ejpam-2985	202	45	the	the	DET
ejpam-2985	202	46	unique	unique	ADJ
ejpam-2985	202	47	common	common	ADJ
ejpam-2985	202	48	fixed	fix	VERB
ejpam-2985	202	49	point	point	NOUN
ejpam-2985	202	50	of	of	ADP
ejpam-2985	202	51	s	s	PROPN
ejpam-2985	202	52	,	,	PUNCT
ejpam-2985	202	53	f	f	PROPN
ejpam-2985	202	54	and	and	CCONJ
ejpam-2985	202	55	g.	g.	PROPN
ejpam-2985	202	56	this	this	PRON
ejpam-2985	202	57	completes	complete	VERB
ejpam-2985	202	58	the	the	DET
ejpam-2985	202	59	proof	proof	NOUN
ejpam-2985	202	60	of	of	ADP
ejpam-2985	202	61	the	the	DET
ejpam-2985	202	62	theorem	theorem	PROPN
ejpam-2985	202	63	.	.	PROPN
ejpam-2985	202	64	example	example	NOUN
ejpam-2985	203	1	1	1	NUM
ejpam-2985	203	2	.	.	PUNCT
ejpam-2985	203	3	let	let	VERB
ejpam-2985	203	4	x	x	PUNCT
ejpam-2985	203	5	=	=	PRON
ejpam-2985	203	6	{	{	PUNCT
ejpam-2985	203	7	1	1	NUM
ejpam-2985	203	8	,	,	PUNCT
ejpam-2985	203	9	2	2	NUM
ejpam-2985	203	10	,	,	PUNCT
ejpam-2985	203	11	3	3	NUM
ejpam-2985	203	12	,	,	PUNCT
ejpam-2985	203	13	4	4	NUM
ejpam-2985	203	14	,	,	PUNCT
ejpam-2985	203	15	5	5	NUM
ejpam-2985	203	16	}	}	PUNCT
ejpam-2985	203	17	,	,	PUNCT
ejpam-2985	203	18	e	e	X
ejpam-2985	203	19	=	=	PUNCT
ejpam-2985	203	20	r2	r2	PROPN
ejpam-2985	203	21	and	and	CCONJ
ejpam-2985	203	22	p	p	NOUN
ejpam-2985	203	23	=	=	X
ejpam-2985	203	24	{	{	PUNCT
ejpam-2985	203	25	(	(	PUNCT
ejpam-2985	203	26	x	x	NOUN
ejpam-2985	203	27	,	,	PUNCT
ejpam-2985	203	28	y	y	PROPN
ejpam-2985	203	29	)	)	PUNCT
ejpam-2985	203	30	:	:	PUNCT
ejpam-2985	204	1	x	x	X
ejpam-2985	204	2	,	,	PUNCT
ejpam-2985	204	3	y	y	PROPN
ejpam-2985	204	4	≥	≥	NOUN
ejpam-2985	204	5	0	0	NUM
ejpam-2985	204	6	}	}	PUNCT
ejpam-2985	204	7	is	be	AUX
ejpam-2985	204	8	a	a	DET
ejpam-2985	204	9	cone	cone	NOUN
ejpam-2985	204	10	in	in	ADP
ejpam-2985	204	11	e.	e.	PROPN
ejpam-2985	204	12	define	define	VERB
ejpam-2985	205	1	d	d	X
ejpam-2985	205	2	:	:	PUNCT
ejpam-2985	205	3	x	x	PROPN
ejpam-2985	205	4	×x	×x	X
ejpam-2985	205	5	→	→	SYM
ejpam-2985	205	6	e	e	NOUN
ejpam-2985	205	7	as	as	SCONJ
ejpam-2985	205	8	follows	follow	VERB
ejpam-2985	205	9	:	:	PUNCT
ejpam-2985	205	10	d(x	d(x	PROPN
ejpam-2985	205	11	,	,	PUNCT
ejpam-2985	205	12	x	x	NOUN
ejpam-2985	205	13	)	)	PUNCT
ejpam-2985	205	14	=	=	SYM
ejpam-2985	206	1	0	0	NUM
ejpam-2985	206	2	,	,	PUNCT
ejpam-2985	206	3	∀x	∀x	VERB
ejpam-2985	206	4	∈	∈	PROPN
ejpam-2985	206	5	x	x	X
ejpam-2985	206	6	;	;	PUNCT
ejpam-2985	207	1	d(1	d(1	VERB
ejpam-2985	207	2	,	,	PUNCT
ejpam-2985	207	3	2	2	NUM
ejpam-2985	207	4	)	)	PUNCT
ejpam-2985	207	5	=	=	SYM
ejpam-2985	207	6	d(2	d(2	PROPN
ejpam-2985	207	7	,	,	PUNCT
ejpam-2985	207	8	1	1	NUM
ejpam-2985	207	9	)	)	PUNCT
ejpam-2985	207	10	=	=	NOUN
ejpam-2985	207	11	(	(	PUNCT
ejpam-2985	207	12	4	4	NUM
ejpam-2985	207	13	,	,	PUNCT
ejpam-2985	207	14	8)	8)	NUM
ejpam-2985	207	15	;	;	PUNCT
ejpam-2985	207	16	d(1	d(1	VERB
ejpam-2985	207	17	,	,	PUNCT
ejpam-2985	207	18	3	3	X
ejpam-2985	207	19	)	)	PUNCT
ejpam-2985	207	20	=	=	SYM
ejpam-2985	208	1	d(3	d(3	PROPN
ejpam-2985	208	2	,	,	PUNCT
ejpam-2985	208	3	1	1	NUM
ejpam-2985	208	4	)	)	PUNCT
ejpam-2985	208	5	=	=	SYM
ejpam-2985	209	1	d(3	d(3	PROPN
ejpam-2985	209	2	,	,	PUNCT
ejpam-2985	209	3	4	4	NUM
ejpam-2985	209	4	)	)	PUNCT
ejpam-2985	209	5	=	=	SYM
ejpam-2985	209	6	d(4	d(4	PROPN
ejpam-2985	209	7	,	,	PUNCT
ejpam-2985	209	8	3	3	NUM
ejpam-2985	209	9	)	)	PUNCT
ejpam-2985	209	10	=	=	SYM
ejpam-2985	210	1	d(2	d(2	PROPN
ejpam-2985	210	2	,	,	PUNCT
ejpam-2985	210	3	4	4	NUM
ejpam-2985	210	4	)	)	PUNCT
ejpam-2985	210	5	=	=	SYM
ejpam-2985	210	6	d(4	d(4	NOUN
ejpam-2985	210	7	,	,	PUNCT
ejpam-2985	210	8	2	2	NUM
ejpam-2985	210	9	)	)	PUNCT
ejpam-2985	210	10	=	=	NOUN
ejpam-2985	210	11	(	(	PUNCT
ejpam-2985	210	12	1	1	NUM
ejpam-2985	210	13	,	,	PUNCT
ejpam-2985	210	14	2	2	NUM
ejpam-2985	210	15	)	)	PUNCT
ejpam-2985	210	16	;	;	PUNCT
ejpam-2985	210	17	d(1	d(1	VERB
ejpam-2985	210	18	,	,	PUNCT
ejpam-2985	210	19	5	5	NUM
ejpam-2985	210	20	)	)	PUNCT
ejpam-2985	210	21	=	=	SYM
ejpam-2985	211	1	d(5	d(5	PROPN
ejpam-2985	211	2	,	,	PUNCT
ejpam-2985	211	3	1	1	NUM
ejpam-2985	211	4	)	)	PUNCT
ejpam-2985	211	5	=	=	SYM
ejpam-2985	212	1	d(2	d(2	PROPN
ejpam-2985	212	2	,	,	PUNCT
ejpam-2985	212	3	5	5	NUM
ejpam-2985	212	4	)	)	PUNCT
ejpam-2985	212	5	=	=	SYM
ejpam-2985	213	1	d(5	d(5	PROPN
ejpam-2985	213	2	,	,	PUNCT
ejpam-2985	213	3	2	2	NUM
ejpam-2985	213	4	)	)	PUNCT
ejpam-2985	213	5	=	=	SYM
ejpam-2985	214	1	d(3	d(3	PROPN
ejpam-2985	214	2	,	,	PUNCT
ejpam-2985	214	3	5	5	NUM
ejpam-2985	214	4	)	)	PUNCT
ejpam-2985	214	5	=	=	SYM
ejpam-2985	214	6	d(5	d(5	PROPN
ejpam-2985	214	7	,	,	PUNCT
ejpam-2985	214	8	3	3	NUM
ejpam-2985	214	9	)	)	PUNCT
ejpam-2985	214	10	=	=	SYM
ejpam-2985	214	11	d(4	d(4	NOUN
ejpam-2985	214	12	,	,	PUNCT
ejpam-2985	214	13	5	5	NUM
ejpam-2985	214	14	)	)	PUNCT
ejpam-2985	214	15	=	=	SYM
ejpam-2985	214	16	d(5	d(5	PROPN
ejpam-2985	214	17	,	,	PUNCT
ejpam-2985	214	18	4	4	NUM
ejpam-2985	214	19	)	)	PUNCT
ejpam-2985	214	20	=	=	NOUN
ejpam-2985	214	21	(	(	PUNCT
ejpam-2985	214	22	3	3	NUM
ejpam-2985	214	23	,	,	PUNCT
ejpam-2985	214	24	6	6	NUM
ejpam-2985	214	25	)	)	PUNCT
ejpam-2985	214	26	.	.	PUNCT
ejpam-2985	215	1	then	then	ADV
ejpam-2985	215	2	(	(	PUNCT
ejpam-2985	215	3	x	x	X
ejpam-2985	215	4	,	,	PUNCT
ejpam-2985	215	5	d	d	NOUN
ejpam-2985	215	6	)	)	PUNCT
ejpam-2985	215	7	is	be	AUX
ejpam-2985	215	8	a	a	DET
ejpam-2985	215	9	cone	cone	NOUN
ejpam-2985	215	10	pentagonal	pentagonal	ADJ
ejpam-2985	215	11	metric	metric	ADJ
ejpam-2985	215	12	space	space	NOUN
ejpam-2985	215	13	,	,	PUNCT
ejpam-2985	215	14	but	but	CCONJ
ejpam-2985	215	15	(	(	PUNCT
ejpam-2985	215	16	x	x	X
ejpam-2985	215	17	,	,	PUNCT
ejpam-2985	215	18	d	d	NOUN
ejpam-2985	215	19	)	)	PUNCT
ejpam-2985	215	20	is	be	AUX
ejpam-2985	215	21	not	not	PART
ejpam-2985	215	22	a	a	DET
ejpam-2985	215	23	cone	cone	NOUN
ejpam-2985	215	24	rectangular	rectangular	ADJ
ejpam-2985	215	25	metric	metric	ADJ
ejpam-2985	215	26	space	space	NOUN
ejpam-2985	215	27	because	because	SCONJ
ejpam-2985	215	28	it	it	PRON
ejpam-2985	215	29	lacks	lack	VERB
ejpam-2985	215	30	the	the	DET
ejpam-2985	215	31	rectangular	rectangular	ADJ
ejpam-2985	215	32	property	property	NOUN
ejpam-2985	215	33	:	:	PUNCT
ejpam-2985	215	34	(	(	PUNCT
ejpam-2985	215	35	4	4	NUM
ejpam-2985	215	36	,	,	PUNCT
ejpam-2985	215	37	8)	8)	NUM
ejpam-2985	215	38	=	=	SYM
ejpam-2985	215	39	d(1	d(1	PROPN
ejpam-2985	215	40	,	,	PUNCT
ejpam-2985	215	41	2	2	NUM
ejpam-2985	215	42	)	)	PUNCT
ejpam-2985	215	43	>	>	X
ejpam-2985	216	1	d(1	d(1	PROPN
ejpam-2985	216	2	,	,	PUNCT
ejpam-2985	216	3	3	3	NUM
ejpam-2985	216	4	)	)	PUNCT
ejpam-2985	216	5	+	+	CCONJ
ejpam-2985	217	1	d(3	d(3	PROPN
ejpam-2985	217	2	,	,	PUNCT
ejpam-2985	217	3	4	4	NUM
ejpam-2985	217	4	)	)	PUNCT
ejpam-2985	217	5	+	+	CCONJ
ejpam-2985	217	6	d(4	d(4	NOUN
ejpam-2985	217	7	,	,	PUNCT
ejpam-2985	217	8	2	2	NUM
ejpam-2985	217	9	)	)	PUNCT
ejpam-2985	217	10	=	=	NOUN
ejpam-2985	217	11	(	(	PUNCT
ejpam-2985	217	12	1	1	NUM
ejpam-2985	217	13	,	,	PUNCT
ejpam-2985	217	14	2	2	NUM
ejpam-2985	217	15	)	)	PUNCT
ejpam-2985	217	16	+	+	CCONJ
ejpam-2985	217	17	(	(	PUNCT
ejpam-2985	217	18	1	1	NUM
ejpam-2985	217	19	,	,	PUNCT
ejpam-2985	217	20	2	2	NUM
ejpam-2985	217	21	)	)	PUNCT
ejpam-2985	217	22	+	+	CCONJ
ejpam-2985	217	23	(	(	PUNCT
ejpam-2985	217	24	1	1	NUM
ejpam-2985	217	25	,	,	PUNCT
ejpam-2985	217	26	2	2	NUM
ejpam-2985	217	27	)	)	PUNCT
ejpam-2985	217	28	=	=	NOUN
ejpam-2985	217	29	(	(	PUNCT
ejpam-2985	217	30	3	3	NUM
ejpam-2985	217	31	,	,	PUNCT
ejpam-2985	217	32	6	6	NUM
ejpam-2985	217	33	)	)	PUNCT
ejpam-2985	217	34	as	as	ADP
ejpam-2985	217	35	(	(	PUNCT
ejpam-2985	217	36	4	4	NUM
ejpam-2985	217	37	,	,	PUNCT
ejpam-2985	217	38	8)−	8)−	NUM
ejpam-2985	217	39	(	(	PUNCT
ejpam-2985	217	40	3	3	NUM
ejpam-2985	217	41	,	,	PUNCT
ejpam-2985	217	42	6	6	NUM
ejpam-2985	217	43	)	)	PUNCT
ejpam-2985	217	44	=	=	SYM
ejpam-2985	217	45	(	(	PUNCT
ejpam-2985	217	46	1	1	NUM
ejpam-2985	217	47	,	,	PUNCT
ejpam-2985	217	48	2	2	NUM
ejpam-2985	217	49	)	)	PUNCT
ejpam-2985	217	50	∈	∈	PROPN
ejpam-2985	217	51	p.	p.	NOUN
ejpam-2985	217	52	define	define	VERB
ejpam-2985	217	53	a	a	DET
ejpam-2985	217	54	mapping	mapping	NOUN
ejpam-2985	217	55	s	s	NOUN
ejpam-2985	217	56	,	,	PUNCT
ejpam-2985	217	57	f	f	PROPN
ejpam-2985	217	58	and	and	CCONJ
ejpam-2985	217	59	g	g	PROPN
ejpam-2985	217	60	:	:	PUNCT
ejpam-2985	217	61	x	x	SYM
ejpam-2985	217	62	→	→	SYM
ejpam-2985	217	63	x	x	PUNCT
ejpam-2985	217	64	as	as	SCONJ
ejpam-2985	217	65	follows	follow	VERB
ejpam-2985	217	66	:	:	PUNCT
ejpam-2985	217	67	s(x	s(x	X
ejpam-2985	217	68	)	)	PUNCT
ejpam-2985	217	69	=	=	SYM
ejpam-2985	218	1	4	4	NUM
ejpam-2985	218	2	,	,	PUNCT
ejpam-2985	218	3	∀x	∀x	X
ejpam-2985	218	4	∈	∈	PROPN
ejpam-2985	218	5	x.	x.	NOUN
ejpam-2985	218	6	f(x	f(x	PROPN
ejpam-2985	218	7	)	)	PUNCT
ejpam-2985	219	1	=	=	PRON
ejpam-2985	219	2	{	{	PUNCT
ejpam-2985	219	3	4	4	NUM
ejpam-2985	219	4	,	,	PUNCT
ejpam-2985	219	5	if	if	SCONJ
ejpam-2985	219	6	x	x	SYM
ejpam-2985	219	7	6=	6=	ADP
ejpam-2985	219	8	5	5	NUM
ejpam-2985	219	9	;	;	PUNCT
ejpam-2985	219	10	2	2	NUM
ejpam-2985	219	11	,	,	PUNCT
ejpam-2985	219	12	if	if	SCONJ
ejpam-2985	219	13	x	x	X
ejpam-2985	219	14	=	=	SYM
ejpam-2985	219	15	5	5	NUM
ejpam-2985	219	16	.	.	PUNCT
ejpam-2985	219	17	g(x	g(x	NOUN
ejpam-2985	219	18	)	)	PUNCT
ejpam-2985	220	1	=	=	SYM
ejpam-2985	220	2	x	x	X
ejpam-2985	220	3	,	,	PUNCT
ejpam-2985	220	4	∀x	∀x	X
ejpam-2985	220	5	∈	∈	PROPN
ejpam-2985	220	6	x.	x.	NOUN
ejpam-2985	220	7	clearly	clearly	ADV
ejpam-2985	220	8	s(x)∪	s(x)∪	VERB
ejpam-2985	220	9	f(x	f(x	PROPN
ejpam-2985	220	10	)	)	PUNCT
ejpam-2985	220	11	⊆	⊆	NUM
ejpam-2985	220	12	g(x	g(x	NOUN
ejpam-2985	220	13	)	)	PUNCT
ejpam-2985	220	14	,	,	PUNCT
ejpam-2985	220	15	g(x	g(x	NOUN
ejpam-2985	220	16	)	)	PUNCT
ejpam-2985	220	17	is	be	AUX
ejpam-2985	220	18	a	a	DET
ejpam-2985	220	19	complete	complete	ADJ
ejpam-2985	220	20	subspace	subspace	NOUN
ejpam-2985	220	21	of	of	ADP
ejpam-2985	220	22	x.	x.	NOUN
ejpam-2985	220	23	also	also	ADV
ejpam-2985	220	24	,	,	PUNCT
ejpam-2985	220	25	the	the	DET
ejpam-2985	220	26	pairs	pair	NOUN
ejpam-2985	220	27	(	(	PUNCT
ejpam-2985	220	28	s	s	X
ejpam-2985	220	29	,	,	PUNCT
ejpam-2985	220	30	g	g	NOUN
ejpam-2985	220	31	)	)	PUNCT
ejpam-2985	220	32	and	and	CCONJ
ejpam-2985	220	33	(	(	PUNCT
ejpam-2985	220	34	f	f	X
ejpam-2985	220	35	,	,	PUNCT
ejpam-2985	220	36	g	g	NOUN
ejpam-2985	220	37	)	)	PUNCT
ejpam-2985	220	38	are	be	AUX
ejpam-2985	220	39	weakly	weakly	ADJ
ejpam-2985	220	40	compatibles	compatible	NOUN
ejpam-2985	220	41	.	.	PUNCT
ejpam-2985	221	1	the	the	DET
ejpam-2985	221	2	conditions	condition	NOUN
ejpam-2985	221	3	of	of	ADP
ejpam-2985	221	4	theorem	theorem	ADJ
ejpam-2985	221	5	1	1	NUM
ejpam-2985	221	6	holds	hold	VERB
ejpam-2985	221	7	for	for	ADP
ejpam-2985	221	8	all	all	DET
ejpam-2985	221	9	x	x	NOUN
ejpam-2985	221	10	,	,	PUNCT
ejpam-2985	221	11	y	y	PROPN
ejpam-2985	221	12	∈	∈	PROPN
ejpam-2985	221	13	x	x	NOUN
ejpam-2985	221	14	,	,	PUNCT
ejpam-2985	221	15	where	where	SCONJ
ejpam-2985	221	16	ϕ(t	ϕ(t	NUM
ejpam-2985	221	17	)	)	PUNCT
ejpam-2985	222	1	=	=	SYM
ejpam-2985	222	2	1	1	NUM
ejpam-2985	222	3	3	3	NUM
ejpam-2985	222	4	t	t	NOUN
ejpam-2985	222	5	,	,	PUNCT
ejpam-2985	222	6	and	and	CCONJ
ejpam-2985	222	7	4	4	NUM
ejpam-2985	222	8	is	be	AUX
ejpam-2985	222	9	the	the	DET
ejpam-2985	222	10	unique	unique	ADJ
ejpam-2985	222	11	common	common	ADJ
ejpam-2985	222	12	fixed	fix	VERB
ejpam-2985	222	13	point	point	NOUN
ejpam-2985	222	14	of	of	ADP
ejpam-2985	222	15	the	the	DET
ejpam-2985	222	16	mappings	mapping	NOUN
ejpam-2985	222	17	s	s	PART
ejpam-2985	222	18	,	,	PUNCT
ejpam-2985	222	19	f	f	PROPN
ejpam-2985	222	20	and	and	CCONJ
ejpam-2985	222	21	g.	g.	PROPN
ejpam-2985	222	22	corollary	corollary	NOUN
ejpam-2985	222	23	1	1	NUM
ejpam-2985	222	24	.	.	PUNCT
ejpam-2985	223	1	let	let	VERB
ejpam-2985	223	2	(	(	PUNCT
ejpam-2985	223	3	x	x	NOUN
ejpam-2985	223	4	,	,	PUNCT
ejpam-2985	223	5	d	d	NOUN
ejpam-2985	223	6	)	)	PUNCT
ejpam-2985	223	7	be	be	AUX
ejpam-2985	223	8	a	a	DET
ejpam-2985	223	9	cone	cone	NOUN
ejpam-2985	223	10	pentagonal	pentagonal	ADJ
ejpam-2985	223	11	metric	metric	ADJ
ejpam-2985	223	12	space	space	NOUN
ejpam-2985	223	13	.	.	PUNCT
ejpam-2985	224	1	suppose	suppose	VERB
ejpam-2985	224	2	the	the	DET
ejpam-2985	224	3	mappings	mapping	NOUN
ejpam-2985	224	4	s	s	PART
ejpam-2985	224	5	,	,	PUNCT
ejpam-2985	224	6	f	f	PROPN
ejpam-2985	224	7	,	,	PUNCT
ejpam-2985	224	8	g	g	NOUN
ejpam-2985	224	9	:	:	PUNCT
ejpam-2985	224	10	x	x	SYM
ejpam-2985	224	11	→	→	PUNCT
ejpam-2985	224	12	x	x	SYM
ejpam-2985	224	13	satisfies	satisfy	VERB
ejpam-2985	224	14	the	the	DET
ejpam-2985	224	15	contractive	contractive	ADJ
ejpam-2985	224	16	condition	condition	NOUN
ejpam-2985	224	17	:	:	PUNCT
ejpam-2985	224	18	d(sx	d(sx	PROPN
ejpam-2985	224	19	,	,	PUNCT
ejpam-2985	224	20	fy	fy	NOUN
ejpam-2985	224	21	)	)	PUNCT
ejpam-2985	224	22	≤	≤	PUNCT
ejpam-2985	225	1	λd(gx	λd(gx	PROPN
ejpam-2985	225	2	,	,	PUNCT
ejpam-2985	225	3	gy	gy	NOUN
ejpam-2985	225	4	)	)	PUNCT
ejpam-2985	225	5	,	,	PUNCT
ejpam-2985	225	6	for	for	ADP
ejpam-2985	225	7	all	all	DET
ejpam-2985	225	8	x	x	NOUN
ejpam-2985	225	9	,	,	PUNCT
ejpam-2985	225	10	y	y	PROPN
ejpam-2985	225	11	∈	∈	PROPN
ejpam-2985	225	12	x	x	NOUN
ejpam-2985	225	13	,	,	PUNCT
ejpam-2985	225	14	where	where	SCONJ
ejpam-2985	225	15	λ	λ	PROPN
ejpam-2985	225	16	∈	∈	PROPN
ejpam-2985	226	1	[	[	X
ejpam-2985	226	2	0	0	NUM
ejpam-2985	226	3	,	,	PUNCT
ejpam-2985	226	4	1	1	NUM
ejpam-2985	226	5	)	)	PUNCT
ejpam-2985	226	6	.	.	PUNCT
ejpam-2985	227	1	suppose	suppose	VERB
ejpam-2985	227	2	that	that	SCONJ
ejpam-2985	227	3	s(x	s(x	NOUN
ejpam-2985	227	4	)	)	PUNCT
ejpam-2985	227	5	∪	∪	ADP
ejpam-2985	227	6	f(x	f(x	PROPN
ejpam-2985	227	7	)	)	PUNCT
ejpam-2985	227	8	⊆	⊆	NUM
ejpam-2985	227	9	g(x	g(x	NOUN
ejpam-2985	227	10	)	)	PUNCT
ejpam-2985	227	11	,	,	PUNCT
ejpam-2985	227	12	and	and	CCONJ
ejpam-2985	227	13	g(x	g(x	NOUN
ejpam-2985	227	14	)	)	PUNCT
ejpam-2985	227	15	is	be	AUX
ejpam-2985	227	16	a	a	DET
ejpam-2985	227	17	complete	complete	ADJ
ejpam-2985	227	18	subspace	subspace	NOUN
ejpam-2985	227	19	of	of	ADP
ejpam-2985	227	20	x	x	PRON
ejpam-2985	227	21	,	,	PUNCT
ejpam-2985	227	22	then	then	ADV
ejpam-2985	227	23	the	the	DET
ejpam-2985	227	24	mappings	mapping	NOUN
ejpam-2985	227	25	s	s	PART
ejpam-2985	227	26	,	,	PUNCT
ejpam-2985	227	27	f	f	PROPN
ejpam-2985	227	28	and	and	CCONJ
ejpam-2985	227	29	g	g	PROPN
ejpam-2985	227	30	have	have	VERB
ejpam-2985	227	31	a	a	DET
ejpam-2985	227	32	unique	unique	ADJ
ejpam-2985	227	33	point	point	NOUN
ejpam-2985	227	34	of	of	ADP
ejpam-2985	227	35	coincidence	coincidence	NOUN
ejpam-2985	227	36	in	in	ADP
ejpam-2985	227	37	x.	x.	NOUN
ejpam-2985	227	38	moreover	moreover	ADV
ejpam-2985	227	39	,	,	PUNCT
ejpam-2985	227	40	if	if	SCONJ
ejpam-2985	227	41	(	(	PUNCT
ejpam-2985	227	42	s	s	X
ejpam-2985	227	43	,	,	PUNCT
ejpam-2985	227	44	g	g	NOUN
ejpam-2985	227	45	)	)	PUNCT
ejpam-2985	227	46	and	and	CCONJ
ejpam-2985	227	47	(	(	PUNCT
ejpam-2985	227	48	f	f	X
ejpam-2985	227	49	,	,	PUNCT
ejpam-2985	227	50	g	g	NOUN
ejpam-2985	227	51	)	)	PUNCT
ejpam-2985	227	52	are	be	AUX
ejpam-2985	227	53	weakly	weakly	ADV
ejpam-2985	227	54	compatible	compatible	ADJ
ejpam-2985	227	55	then	then	ADV
ejpam-2985	227	56	s	s	PROPN
ejpam-2985	227	57	,	,	PUNCT
ejpam-2985	227	58	f	f	PROPN
ejpam-2985	227	59	and	and	CCONJ
ejpam-2985	227	60	g	g	PROPN
ejpam-2985	227	61	have	have	VERB
ejpam-2985	227	62	a	a	DET
ejpam-2985	227	63	unique	unique	ADJ
ejpam-2985	227	64	common	common	ADJ
ejpam-2985	227	65	fixed	fix	VERB
ejpam-2985	227	66	point	point	NOUN
ejpam-2985	227	67	in	in	ADP
ejpam-2985	227	68	x.	x.	NOUN
ejpam-2985	227	69	proof	proof	NOUN
ejpam-2985	227	70	.	.	PUNCT
ejpam-2985	228	1	define	define	VERB
ejpam-2985	228	2	ϕ	ϕ	NOUN
ejpam-2985	228	3	:	:	PUNCT
ejpam-2985	228	4	p	p	X
ejpam-2985	228	5	→	→	PUNCT
ejpam-2985	228	6	p	p	NOUN
ejpam-2985	228	7	by	by	ADP
ejpam-2985	228	8	ϕ(t	ϕ(t	NUM
ejpam-2985	228	9	)	)	PUNCT
ejpam-2985	229	1	=	=	SYM
ejpam-2985	230	1	λt	λt	ADP
ejpam-2985	230	2	.	.	PUNCT
ejpam-2985	231	1	then	then	ADV
ejpam-2985	231	2	it	it	PRON
ejpam-2985	231	3	is	be	AUX
ejpam-2985	231	4	clear	clear	ADJ
ejpam-2985	231	5	that	that	SCONJ
ejpam-2985	231	6	ϕ	ϕ	PROPN
ejpam-2985	231	7	satisfies	satisfy	VERB
ejpam-2985	231	8	the	the	DET
ejpam-2985	231	9	conditions	condition	NOUN
ejpam-2985	231	10	in	in	ADP
ejpam-2985	231	11	definition	definition	NOUN
ejpam-2985	231	12	5	5	NUM
ejpam-2985	231	13	.	.	PUNCT
ejpam-2985	232	1	hence	hence	ADV
ejpam-2985	232	2	the	the	DET
ejpam-2985	232	3	results	result	NOUN
ejpam-2985	232	4	follows	follow	VERB
ejpam-2985	232	5	from	from	ADP
ejpam-2985	232	6	theorem	theorem	ADJ
ejpam-2985	232	7	1	1	NUM
ejpam-2985	232	8	.	.	PUNCT
ejpam-2985	232	9	a.	a.	NOUN
ejpam-2985	232	10	auwalu	auwalu	PROPN
ejpam-2985	232	11	,	,	PUNCT
ejpam-2985	232	12	e.	e.	PROPN
ejpam-2985	232	13	hınçal	hınçal	PROPN
ejpam-2985	232	14	/	/	SYM
ejpam-2985	232	15	eur	eur	PROPN
ejpam-2985	232	16	.	.	PUNCT
ejpam-2985	233	1	j.	j.	PROPN
ejpam-2985	233	2	pure	pure	PROPN
ejpam-2985	233	3	appl	appl	PROPN
ejpam-2985	233	4	.	.	PROPN
ejpam-2985	233	5	math	math	PROPN
ejpam-2985	233	6	,	,	PUNCT
ejpam-2985	233	7	10	10	NUM
ejpam-2985	233	8	(	(	PUNCT
ejpam-2985	233	9	3	3	NUM
ejpam-2985	233	10	)	)	PUNCT
ejpam-2985	233	11	(	(	PUNCT
ejpam-2985	233	12	2017	2017	NUM
ejpam-2985	233	13	)	)	PUNCT
ejpam-2985	233	14	,	,	PUNCT
ejpam-2985	233	15	473	473	NUM
ejpam-2985	233	16	-	-	SYM
ejpam-2985	233	17	487	487	NUM
ejpam-2985	233	18	481	481	NUM
ejpam-2985	233	19	corollary	corollary	ADJ
ejpam-2985	233	20	2	2	NUM
ejpam-2985	233	21	.	.	PUNCT
ejpam-2985	234	1	(	(	PUNCT
ejpam-2985	234	2	see	see	VERB
ejpam-2985	234	3	[	[	X
ejpam-2985	234	4	4	4	NUM
ejpam-2985	234	5	]	]	PUNCT
ejpam-2985	234	6	)	)	PUNCT
ejpam-2985	234	7	let	let	VERB
ejpam-2985	234	8	(	(	PUNCT
ejpam-2985	234	9	x	x	NOUN
ejpam-2985	234	10	,	,	PUNCT
ejpam-2985	234	11	d	d	NOUN
ejpam-2985	234	12	)	)	PUNCT
ejpam-2985	234	13	be	be	AUX
ejpam-2985	234	14	a	a	DET
ejpam-2985	234	15	cone	cone	NOUN
ejpam-2985	234	16	pentagonal	pentagonal	ADJ
ejpam-2985	234	17	metric	metric	ADJ
ejpam-2985	234	18	space	space	NOUN
ejpam-2985	234	19	.	.	PUNCT
ejpam-2985	235	1	suppose	suppose	VERB
ejpam-2985	235	2	the	the	DET
ejpam-2985	235	3	mappings	mapping	NOUN
ejpam-2985	235	4	s	s	PART
ejpam-2985	235	5	,	,	PUNCT
ejpam-2985	235	6	g	g	NOUN
ejpam-2985	235	7	:	:	PUNCT
ejpam-2985	235	8	x	x	SYM
ejpam-2985	235	9	→	→	PUNCT
ejpam-2985	235	10	x	x	SYM
ejpam-2985	235	11	satisfies	satisfy	VERB
ejpam-2985	235	12	the	the	DET
ejpam-2985	235	13	contractive	contractive	ADJ
ejpam-2985	235	14	condition	condition	NOUN
ejpam-2985	235	15	:	:	PUNCT
ejpam-2985	235	16	d(sx	d(sx	NOUN
ejpam-2985	235	17	,	,	PUNCT
ejpam-2985	235	18	sy	sy	NOUN
ejpam-2985	235	19	)	)	PUNCT
ejpam-2985	235	20	≤	≤	NOUN
ejpam-2985	235	21	ϕ	ϕ	X
ejpam-2985	235	22	(	(	PUNCT
ejpam-2985	235	23	d(gx	d(gx	PROPN
ejpam-2985	235	24	,	,	PUNCT
ejpam-2985	235	25	gy	gy	NOUN
ejpam-2985	235	26	)	)	PUNCT
ejpam-2985	235	27	)	)	PUNCT
ejpam-2985	235	28	,	,	PUNCT
ejpam-2985	235	29	for	for	ADP
ejpam-2985	235	30	all	all	DET
ejpam-2985	235	31	x	x	NOUN
ejpam-2985	235	32	,	,	PUNCT
ejpam-2985	235	33	y	y	PROPN
ejpam-2985	235	34	∈	∈	PROPN
ejpam-2985	235	35	x	x	NOUN
ejpam-2985	235	36	,	,	PUNCT
ejpam-2985	235	37	where	where	SCONJ
ejpam-2985	235	38	ϕ	ϕ	PROPN
ejpam-2985	235	39	∈	∈	PROPN
ejpam-2985	235	40	φ	φ	PROPN
ejpam-2985	235	41	.	.	PUNCT
ejpam-2985	235	42	suppose	suppose	VERB
ejpam-2985	235	43	that	that	SCONJ
ejpam-2985	235	44	s(x	s(x	NOUN
ejpam-2985	235	45	)	)	PUNCT
ejpam-2985	235	46	⊆	⊆	NUM
ejpam-2985	235	47	g(x	g(x	NOUN
ejpam-2985	235	48	)	)	PUNCT
ejpam-2985	235	49	,	,	PUNCT
ejpam-2985	235	50	and	and	CCONJ
ejpam-2985	235	51	g(x	g(x	NOUN
ejpam-2985	235	52	)	)	PUNCT
ejpam-2985	235	53	or	or	CCONJ
ejpam-2985	235	54	s(x	s(x	NOUN
ejpam-2985	235	55	)	)	PUNCT
ejpam-2985	235	56	is	be	AUX
ejpam-2985	235	57	a	a	DET
ejpam-2985	235	58	complete	complete	ADJ
ejpam-2985	235	59	subspace	subspace	NOUN
ejpam-2985	235	60	of	of	ADP
ejpam-2985	235	61	x	x	PRON
ejpam-2985	235	62	,	,	PUNCT
ejpam-2985	235	63	then	then	ADV
ejpam-2985	235	64	the	the	DET
ejpam-2985	235	65	mappings	mapping	NOUN
ejpam-2985	235	66	s	s	PART
ejpam-2985	235	67	and	and	CCONJ
ejpam-2985	235	68	g	g	PROPN
ejpam-2985	235	69	have	have	VERB
ejpam-2985	235	70	a	a	DET
ejpam-2985	235	71	unique	unique	ADJ
ejpam-2985	235	72	point	point	NOUN
ejpam-2985	235	73	of	of	ADP
ejpam-2985	235	74	coincidence	coincidence	NOUN
ejpam-2985	235	75	in	in	ADP
ejpam-2985	235	76	x.	x.	NOUN
ejpam-2985	235	77	moreover	moreover	ADV
ejpam-2985	235	78	,	,	PUNCT
ejpam-2985	235	79	if	if	SCONJ
ejpam-2985	235	80	s	s	X
ejpam-2985	235	81	and	and	CCONJ
ejpam-2985	235	82	g	g	PROPN
ejpam-2985	235	83	are	be	AUX
ejpam-2985	235	84	weakly	weakly	ADV
ejpam-2985	235	85	compatible	compatible	ADJ
ejpam-2985	236	1	then	then	ADV
ejpam-2985	236	2	s	s	VERB
ejpam-2985	236	3	and	and	CCONJ
ejpam-2985	236	4	g	g	PROPN
ejpam-2985	236	5	have	have	VERB
ejpam-2985	236	6	a	a	DET
ejpam-2985	236	7	unique	unique	ADJ
ejpam-2985	236	8	common	common	ADJ
ejpam-2985	236	9	fixed	fix	VERB
ejpam-2985	236	10	point	point	NOUN
ejpam-2985	236	11	in	in	ADP
ejpam-2985	236	12	x.	x.	NOUN
ejpam-2985	236	13	proof	proof	NOUN
ejpam-2985	236	14	.	.	PUNCT
ejpam-2985	237	1	putting	put	VERB
ejpam-2985	237	2	f	f	NOUN
ejpam-2985	237	3	=	=	SYM
ejpam-2985	237	4	s	s	PROPN
ejpam-2985	237	5	in	in	ADP
ejpam-2985	237	6	theorem	theorem	NOUN
ejpam-2985	237	7	1	1	NUM
ejpam-2985	237	8	.	.	PUNCT
ejpam-2985	238	1	this	this	PRON
ejpam-2985	238	2	completes	complete	VERB
ejpam-2985	238	3	the	the	DET
ejpam-2985	238	4	proof	proof	NOUN
ejpam-2985	238	5	.	.	PUNCT
ejpam-2985	239	1	corollary	corollary	ADJ
ejpam-2985	239	2	3	3	X
ejpam-2985	239	3	.	.	PUNCT
ejpam-2985	240	1	let	let	VERB
ejpam-2985	240	2	(	(	PUNCT
ejpam-2985	240	3	x	x	NOUN
ejpam-2985	240	4	,	,	PUNCT
ejpam-2985	240	5	d	d	NOUN
ejpam-2985	240	6	)	)	PUNCT
ejpam-2985	240	7	be	be	AUX
ejpam-2985	240	8	a	a	DET
ejpam-2985	240	9	cone	cone	NOUN
ejpam-2985	240	10	pentagonal	pentagonal	ADJ
ejpam-2985	240	11	metric	metric	ADJ
ejpam-2985	240	12	space	space	NOUN
ejpam-2985	240	13	.	.	PUNCT
ejpam-2985	241	1	suppose	suppose	VERB
ejpam-2985	241	2	the	the	DET
ejpam-2985	241	3	mappings	mapping	NOUN
ejpam-2985	241	4	s	s	PART
ejpam-2985	241	5	,	,	PUNCT
ejpam-2985	241	6	g	g	NOUN
ejpam-2985	241	7	:	:	PUNCT
ejpam-2985	241	8	x	x	SYM
ejpam-2985	241	9	→	→	PUNCT
ejpam-2985	241	10	x	x	SYM
ejpam-2985	241	11	satisfies	satisfy	VERB
ejpam-2985	241	12	the	the	DET
ejpam-2985	241	13	contractive	contractive	ADJ
ejpam-2985	241	14	condition	condition	NOUN
ejpam-2985	241	15	:	:	PUNCT
ejpam-2985	241	16	d(sx	d(sx	NOUN
ejpam-2985	241	17	,	,	PUNCT
ejpam-2985	241	18	sy	sy	NOUN
ejpam-2985	241	19	)	)	PUNCT
ejpam-2985	241	20	≤	≤	NOUN
ejpam-2985	241	21	λd(gx	λd(gx	PROPN
ejpam-2985	241	22	,	,	PUNCT
ejpam-2985	241	23	gy	gy	NOUN
ejpam-2985	241	24	)	)	PUNCT
ejpam-2985	241	25	,	,	PUNCT
ejpam-2985	241	26	for	for	ADP
ejpam-2985	241	27	all	all	DET
ejpam-2985	241	28	x	x	NOUN
ejpam-2985	241	29	,	,	PUNCT
ejpam-2985	241	30	y	y	PROPN
ejpam-2985	241	31	∈	∈	PROPN
ejpam-2985	241	32	x	x	NOUN
ejpam-2985	241	33	,	,	PUNCT
ejpam-2985	241	34	where	where	SCONJ
ejpam-2985	241	35	λ	λ	PROPN
ejpam-2985	241	36	∈	∈	PROPN
ejpam-2985	241	37	[	[	X
ejpam-2985	241	38	0	0	NUM
ejpam-2985	241	39	,	,	PUNCT
ejpam-2985	241	40	1	1	NUM
ejpam-2985	241	41	)	)	PUNCT
ejpam-2985	241	42	.	.	PUNCT
ejpam-2985	242	1	suppose	suppose	VERB
ejpam-2985	242	2	that	that	SCONJ
ejpam-2985	242	3	s(x	s(x	NOUN
ejpam-2985	242	4	)	)	PUNCT
ejpam-2985	242	5	⊆	⊆	NUM
ejpam-2985	242	6	g(x	g(x	NOUN
ejpam-2985	242	7	)	)	PUNCT
ejpam-2985	242	8	,	,	PUNCT
ejpam-2985	242	9	and	and	CCONJ
ejpam-2985	242	10	g(x	g(x	NOUN
ejpam-2985	242	11	)	)	PUNCT
ejpam-2985	242	12	or	or	CCONJ
ejpam-2985	242	13	s(x	s(x	NOUN
ejpam-2985	242	14	)	)	PUNCT
ejpam-2985	242	15	is	be	AUX
ejpam-2985	242	16	a	a	DET
ejpam-2985	242	17	complete	complete	ADJ
ejpam-2985	242	18	subspace	subspace	NOUN
ejpam-2985	242	19	of	of	ADP
ejpam-2985	242	20	x	x	PRON
ejpam-2985	242	21	,	,	PUNCT
ejpam-2985	242	22	then	then	ADV
ejpam-2985	242	23	the	the	DET
ejpam-2985	242	24	mappings	mapping	NOUN
ejpam-2985	242	25	s	s	PART
ejpam-2985	242	26	and	and	CCONJ
ejpam-2985	242	27	g	g	PROPN
ejpam-2985	242	28	have	have	VERB
ejpam-2985	242	29	a	a	DET
ejpam-2985	242	30	unique	unique	ADJ
ejpam-2985	242	31	point	point	NOUN
ejpam-2985	242	32	of	of	ADP
ejpam-2985	242	33	coincidence	coincidence	NOUN
ejpam-2985	242	34	in	in	ADP
ejpam-2985	242	35	x.	x.	NOUN
ejpam-2985	242	36	moreover	moreover	ADV
ejpam-2985	242	37	,	,	PUNCT
ejpam-2985	242	38	if	if	SCONJ
ejpam-2985	242	39	s	s	X
ejpam-2985	242	40	and	and	CCONJ
ejpam-2985	242	41	g	g	PROPN
ejpam-2985	242	42	are	be	AUX
ejpam-2985	242	43	weakly	weakly	ADV
ejpam-2985	242	44	compatible	compatible	ADJ
ejpam-2985	242	45	then	then	ADV
ejpam-2985	242	46	s	s	VERB
ejpam-2985	242	47	and	and	CCONJ
ejpam-2985	242	48	g	g	PROPN
ejpam-2985	242	49	have	have	VERB
ejpam-2985	242	50	a	a	DET
ejpam-2985	242	51	unique	unique	ADJ
ejpam-2985	242	52	common	common	ADJ
ejpam-2985	242	53	fixed	fix	VERB
ejpam-2985	242	54	point	point	NOUN
ejpam-2985	242	55	in	in	ADP
ejpam-2985	242	56	x.	x.	NOUN
ejpam-2985	242	57	proof	proof	NOUN
ejpam-2985	242	58	.	.	PUNCT
ejpam-2985	243	1	putting	put	VERB
ejpam-2985	243	2	f	f	NOUN
ejpam-2985	243	3	=	=	SYM
ejpam-2985	243	4	s	s	PROPN
ejpam-2985	243	5	in	in	ADP
ejpam-2985	243	6	theorem	theorem	NOUN
ejpam-2985	243	7	1	1	NUM
ejpam-2985	243	8	.	.	PUNCT
ejpam-2985	244	1	the	the	DET
ejpam-2985	244	2	results	result	NOUN
ejpam-2985	244	3	follows	follow	VERB
ejpam-2985	244	4	from	from	ADP
ejpam-2985	244	5	corollary	corollary	ADJ
ejpam-2985	244	6	1	1	NUM
ejpam-2985	244	7	.	.	PUNCT
ejpam-2985	244	8	corollary	corollary	ADJ
ejpam-2985	244	9	4	4	NUM
ejpam-2985	244	10	.	.	PUNCT
ejpam-2985	245	1	(	(	PUNCT
ejpam-2985	245	2	see	see	VERB
ejpam-2985	245	3	[	[	X
ejpam-2985	245	4	16	16	NUM
ejpam-2985	245	5	]	]	PUNCT
ejpam-2985	245	6	)	)	PUNCT
ejpam-2985	245	7	let	let	VERB
ejpam-2985	245	8	(	(	PUNCT
ejpam-2985	245	9	x	x	NOUN
ejpam-2985	245	10	,	,	PUNCT
ejpam-2985	245	11	d	d	NOUN
ejpam-2985	245	12	)	)	PUNCT
ejpam-2985	245	13	be	be	AUX
ejpam-2985	245	14	a	a	DET
ejpam-2985	245	15	cone	cone	NOUN
ejpam-2985	245	16	rectangular	rectangular	ADJ
ejpam-2985	245	17	metric	metric	ADJ
ejpam-2985	245	18	space	space	NOUN
ejpam-2985	245	19	.	.	PUNCT
ejpam-2985	246	1	suppose	suppose	VERB
ejpam-2985	246	2	the	the	DET
ejpam-2985	246	3	mappings	mapping	NOUN
ejpam-2985	246	4	s	s	PART
ejpam-2985	246	5	,	,	PUNCT
ejpam-2985	246	6	f	f	PROPN
ejpam-2985	246	7	,	,	PUNCT
ejpam-2985	246	8	g	g	NOUN
ejpam-2985	246	9	:	:	PUNCT
ejpam-2985	246	10	x	x	SYM
ejpam-2985	246	11	→	→	PUNCT
ejpam-2985	246	12	x	x	SYM
ejpam-2985	246	13	satisfies	satisfy	VERB
ejpam-2985	246	14	the	the	DET
ejpam-2985	246	15	contractive	contractive	ADJ
ejpam-2985	246	16	condition	condition	NOUN
ejpam-2985	246	17	:	:	PUNCT
ejpam-2985	246	18	d(sx	d(sx	PROPN
ejpam-2985	246	19	,	,	PUNCT
ejpam-2985	246	20	fy	fy	NOUN
ejpam-2985	246	21	)	)	PUNCT
ejpam-2985	246	22	≤	≤	PUNCT
ejpam-2985	247	1	λd(gx	λd(gx	PROPN
ejpam-2985	247	2	,	,	PUNCT
ejpam-2985	247	3	gy	gy	NOUN
ejpam-2985	247	4	)	)	PUNCT
ejpam-2985	247	5	,	,	PUNCT
ejpam-2985	247	6	for	for	ADP
ejpam-2985	247	7	all	all	DET
ejpam-2985	247	8	x	x	NOUN
ejpam-2985	247	9	,	,	PUNCT
ejpam-2985	247	10	y	y	PROPN
ejpam-2985	247	11	∈	∈	PROPN
ejpam-2985	247	12	x	x	NOUN
ejpam-2985	247	13	,	,	PUNCT
ejpam-2985	247	14	where	where	SCONJ
ejpam-2985	247	15	λ	λ	PROPN
ejpam-2985	247	16	∈	∈	PROPN
ejpam-2985	248	1	[	[	X
ejpam-2985	248	2	0	0	NUM
ejpam-2985	248	3	,	,	PUNCT
ejpam-2985	248	4	1	1	NUM
ejpam-2985	248	5	)	)	PUNCT
ejpam-2985	248	6	.	.	PUNCT
ejpam-2985	249	1	suppose	suppose	VERB
ejpam-2985	249	2	that	that	SCONJ
ejpam-2985	249	3	s(x	s(x	NOUN
ejpam-2985	249	4	)	)	PUNCT
ejpam-2985	249	5	∪	∪	ADP
ejpam-2985	249	6	f(x	f(x	PROPN
ejpam-2985	249	7	)	)	PUNCT
ejpam-2985	249	8	⊆	⊆	NUM
ejpam-2985	249	9	g(x	g(x	NOUN
ejpam-2985	249	10	)	)	PUNCT
ejpam-2985	249	11	,	,	PUNCT
ejpam-2985	249	12	and	and	CCONJ
ejpam-2985	249	13	g(x	g(x	NOUN
ejpam-2985	249	14	)	)	PUNCT
ejpam-2985	249	15	is	be	AUX
ejpam-2985	249	16	a	a	DET
ejpam-2985	249	17	complete	complete	ADJ
ejpam-2985	249	18	subspace	subspace	NOUN
ejpam-2985	249	19	of	of	ADP
ejpam-2985	249	20	x	x	PRON
ejpam-2985	249	21	,	,	PUNCT
ejpam-2985	249	22	then	then	ADV
ejpam-2985	249	23	the	the	DET
ejpam-2985	249	24	mappings	mapping	NOUN
ejpam-2985	249	25	s	s	PART
ejpam-2985	249	26	,	,	PUNCT
ejpam-2985	249	27	f	f	PROPN
ejpam-2985	249	28	and	and	CCONJ
ejpam-2985	249	29	g	g	PROPN
ejpam-2985	249	30	have	have	VERB
ejpam-2985	249	31	a	a	DET
ejpam-2985	249	32	unique	unique	ADJ
ejpam-2985	249	33	point	point	NOUN
ejpam-2985	249	34	of	of	ADP
ejpam-2985	249	35	coincidence	coincidence	NOUN
ejpam-2985	249	36	in	in	ADP
ejpam-2985	249	37	x.	x.	NOUN
ejpam-2985	249	38	moreover	moreover	ADV
ejpam-2985	249	39	,	,	PUNCT
ejpam-2985	249	40	if	if	SCONJ
ejpam-2985	249	41	(	(	PUNCT
ejpam-2985	249	42	s	s	X
ejpam-2985	249	43	,	,	PUNCT
ejpam-2985	249	44	g	g	NOUN
ejpam-2985	249	45	)	)	PUNCT
ejpam-2985	249	46	and	and	CCONJ
ejpam-2985	249	47	(	(	PUNCT
ejpam-2985	249	48	f	f	X
ejpam-2985	249	49	,	,	PUNCT
ejpam-2985	249	50	g	g	NOUN
ejpam-2985	249	51	)	)	PUNCT
ejpam-2985	249	52	are	be	AUX
ejpam-2985	249	53	weakly	weakly	ADV
ejpam-2985	249	54	compatible	compatible	ADJ
ejpam-2985	249	55	then	then	ADV
ejpam-2985	249	56	s	s	PROPN
ejpam-2985	249	57	,	,	PUNCT
ejpam-2985	249	58	f	f	PROPN
ejpam-2985	249	59	and	and	CCONJ
ejpam-2985	249	60	g	g	PROPN
ejpam-2985	249	61	have	have	VERB
ejpam-2985	249	62	a	a	DET
ejpam-2985	249	63	unique	unique	ADJ
ejpam-2985	249	64	common	common	ADJ
ejpam-2985	249	65	fixed	fix	VERB
ejpam-2985	249	66	point	point	NOUN
ejpam-2985	249	67	in	in	ADP
ejpam-2985	249	68	x.	x.	NOUN
ejpam-2985	249	69	proof	proof	NOUN
ejpam-2985	249	70	.	.	PUNCT
ejpam-2985	250	1	this	this	PRON
ejpam-2985	250	2	follows	follow	VERB
ejpam-2985	250	3	from	from	ADP
ejpam-2985	250	4	the	the	DET
ejpam-2985	250	5	remark	remark	NOUN
ejpam-2985	250	6	2	2	NUM
ejpam-2985	250	7	and	and	CCONJ
ejpam-2985	250	8	theorem	theorem	VERB
ejpam-2985	250	9	1	1	NUM
ejpam-2985	250	10	.	.	PUNCT
ejpam-2985	250	11	corollary	corollary	ADJ
ejpam-2985	250	12	5	5	NUM
ejpam-2985	250	13	.	.	PUNCT
ejpam-2985	251	1	(	(	PUNCT
ejpam-2985	251	2	see	see	VERB
ejpam-2985	251	3	[	[	X
ejpam-2985	251	4	17	17	NUM
ejpam-2985	251	5	]	]	PUNCT
ejpam-2985	251	6	)	)	PUNCT
ejpam-2985	251	7	let	let	VERB
ejpam-2985	251	8	(	(	PUNCT
ejpam-2985	251	9	x	x	NOUN
ejpam-2985	251	10	,	,	PUNCT
ejpam-2985	251	11	d	d	NOUN
ejpam-2985	251	12	)	)	PUNCT
ejpam-2985	251	13	be	be	AUX
ejpam-2985	251	14	a	a	DET
ejpam-2985	251	15	cone	cone	NOUN
ejpam-2985	251	16	rectangular	rectangular	ADJ
ejpam-2985	251	17	metric	metric	ADJ
ejpam-2985	251	18	space	space	NOUN
ejpam-2985	251	19	.	.	PUNCT
ejpam-2985	252	1	suppose	suppose	VERB
ejpam-2985	252	2	the	the	DET
ejpam-2985	252	3	mappings	mapping	NOUN
ejpam-2985	252	4	s	s	PART
ejpam-2985	252	5	,	,	PUNCT
ejpam-2985	252	6	g	g	NOUN
ejpam-2985	252	7	:	:	PUNCT
ejpam-2985	252	8	x	x	SYM
ejpam-2985	252	9	→	→	PUNCT
ejpam-2985	252	10	x	x	SYM
ejpam-2985	252	11	satisfies	satisfy	VERB
ejpam-2985	252	12	the	the	DET
ejpam-2985	252	13	contractive	contractive	ADJ
ejpam-2985	252	14	condition	condition	NOUN
ejpam-2985	252	15	:	:	PUNCT
ejpam-2985	252	16	d(sx	d(sx	NOUN
ejpam-2985	252	17	,	,	PUNCT
ejpam-2985	252	18	sy	sy	NOUN
ejpam-2985	252	19	)	)	PUNCT
ejpam-2985	252	20	≤	≤	NOUN
ejpam-2985	252	21	ϕ	ϕ	X
ejpam-2985	252	22	(	(	PUNCT
ejpam-2985	252	23	d(gx	d(gx	PROPN
ejpam-2985	252	24	,	,	PUNCT
ejpam-2985	252	25	gy	gy	NOUN
ejpam-2985	252	26	)	)	PUNCT
ejpam-2985	252	27	)	)	PUNCT
ejpam-2985	252	28	,	,	PUNCT
ejpam-2985	252	29	for	for	ADP
ejpam-2985	252	30	all	all	DET
ejpam-2985	252	31	x	x	NOUN
ejpam-2985	252	32	,	,	PUNCT
ejpam-2985	252	33	y	y	PROPN
ejpam-2985	252	34	∈	∈	PROPN
ejpam-2985	252	35	x	x	NOUN
ejpam-2985	252	36	,	,	PUNCT
ejpam-2985	252	37	where	where	SCONJ
ejpam-2985	252	38	ϕ	ϕ	PROPN
ejpam-2985	252	39	∈	∈	PROPN
ejpam-2985	252	40	φ	φ	PROPN
ejpam-2985	252	41	.	.	PUNCT
ejpam-2985	252	42	suppose	suppose	VERB
ejpam-2985	252	43	that	that	SCONJ
ejpam-2985	252	44	s(x	s(x	NOUN
ejpam-2985	252	45	)	)	PUNCT
ejpam-2985	252	46	⊆	⊆	NUM
ejpam-2985	252	47	g(x	g(x	NOUN
ejpam-2985	252	48	)	)	PUNCT
ejpam-2985	252	49	,	,	PUNCT
ejpam-2985	252	50	and	and	CCONJ
ejpam-2985	252	51	g(x	g(x	NOUN
ejpam-2985	252	52	)	)	PUNCT
ejpam-2985	252	53	or	or	CCONJ
ejpam-2985	252	54	s(x	s(x	NOUN
ejpam-2985	252	55	)	)	PUNCT
ejpam-2985	252	56	is	be	AUX
ejpam-2985	252	57	a	a	DET
ejpam-2985	252	58	complete	complete	ADJ
ejpam-2985	252	59	subspace	subspace	NOUN
ejpam-2985	252	60	of	of	ADP
ejpam-2985	252	61	x	x	PRON
ejpam-2985	252	62	,	,	PUNCT
ejpam-2985	252	63	then	then	ADV
ejpam-2985	252	64	the	the	DET
ejpam-2985	252	65	mappings	mapping	NOUN
ejpam-2985	252	66	s	s	PART
ejpam-2985	252	67	and	and	CCONJ
ejpam-2985	252	68	g	g	PROPN
ejpam-2985	252	69	have	have	VERB
ejpam-2985	252	70	a	a	DET
ejpam-2985	252	71	unique	unique	ADJ
ejpam-2985	252	72	point	point	NOUN
ejpam-2985	252	73	of	of	ADP
ejpam-2985	252	74	coincidence	coincidence	NOUN
ejpam-2985	252	75	in	in	ADP
ejpam-2985	252	76	x.	x.	NOUN
ejpam-2985	252	77	moreover	moreover	ADV
ejpam-2985	252	78	,	,	PUNCT
ejpam-2985	252	79	if	if	SCONJ
ejpam-2985	252	80	s	s	X
ejpam-2985	252	81	and	and	CCONJ
ejpam-2985	252	82	g	g	PROPN
ejpam-2985	252	83	are	be	AUX
ejpam-2985	252	84	weakly	weakly	ADV
ejpam-2985	252	85	compatible	compatible	ADJ
ejpam-2985	253	1	then	then	ADV
ejpam-2985	253	2	s	s	VERB
ejpam-2985	253	3	and	and	CCONJ
ejpam-2985	253	4	g	g	PROPN
ejpam-2985	253	5	have	have	VERB
ejpam-2985	253	6	a	a	DET
ejpam-2985	253	7	unique	unique	ADJ
ejpam-2985	253	8	common	common	ADJ
ejpam-2985	253	9	fixed	fix	VERB
ejpam-2985	253	10	point	point	NOUN
ejpam-2985	253	11	in	in	ADP
ejpam-2985	253	12	x.	x.	PROPN
ejpam-2985	253	13	a.	a.	PROPN
ejpam-2985	253	14	auwalu	auwalu	PROPN
ejpam-2985	253	15	,	,	PUNCT
ejpam-2985	253	16	e.	e.	PROPN
ejpam-2985	253	17	hınçal	hınçal	PROPN
ejpam-2985	253	18	/	/	SYM
ejpam-2985	253	19	eur	eur	PROPN
ejpam-2985	253	20	.	.	PUNCT
ejpam-2985	254	1	j.	j.	PROPN
ejpam-2985	254	2	pure	pure	PROPN
ejpam-2985	254	3	appl	appl	PROPN
ejpam-2985	254	4	.	.	PROPN
ejpam-2985	254	5	math	math	PROPN
ejpam-2985	254	6	,	,	PUNCT
ejpam-2985	254	7	10	10	NUM
ejpam-2985	254	8	(	(	PUNCT
ejpam-2985	254	9	3	3	NUM
ejpam-2985	254	10	)	)	PUNCT
ejpam-2985	254	11	(	(	PUNCT
ejpam-2985	254	12	2017	2017	NUM
ejpam-2985	254	13	)	)	PUNCT
ejpam-2985	254	14	,	,	PUNCT
ejpam-2985	254	15	473	473	NUM
ejpam-2985	254	16	-	-	SYM
ejpam-2985	254	17	487	487	NUM
ejpam-2985	254	18	482	482	NUM
ejpam-2985	254	19	proof	proof	NOUN
ejpam-2985	254	20	.	.	PUNCT
ejpam-2985	255	1	this	this	PRON
ejpam-2985	255	2	follows	follow	VERB
ejpam-2985	255	3	from	from	ADP
ejpam-2985	255	4	the	the	DET
ejpam-2985	255	5	remark	remark	NOUN
ejpam-2985	255	6	2	2	NUM
ejpam-2985	255	7	and	and	CCONJ
ejpam-2985	255	8	corollary	corollary	ADJ
ejpam-2985	255	9	2	2	NUM
ejpam-2985	255	10	.	.	PUNCT
ejpam-2985	255	11	corollary	corollary	ADJ
ejpam-2985	255	12	6	6	NUM
ejpam-2985	255	13	.	.	PUNCT
ejpam-2985	256	1	(	(	PUNCT
ejpam-2985	256	2	see	see	VERB
ejpam-2985	256	3	[	[	X
ejpam-2985	256	4	2	2	NUM
ejpam-2985	256	5	]	]	PUNCT
ejpam-2985	256	6	)	)	PUNCT
ejpam-2985	256	7	let	let	VERB
ejpam-2985	256	8	(	(	PUNCT
ejpam-2985	256	9	x	x	NOUN
ejpam-2985	256	10	,	,	PUNCT
ejpam-2985	256	11	d	d	NOUN
ejpam-2985	256	12	)	)	PUNCT
ejpam-2985	256	13	be	be	AUX
ejpam-2985	256	14	a	a	DET
ejpam-2985	256	15	cone	cone	NOUN
ejpam-2985	256	16	pentagonal	pentagonal	ADJ
ejpam-2985	256	17	metric	metric	ADJ
ejpam-2985	256	18	space	space	NOUN
ejpam-2985	256	19	.	.	PUNCT
ejpam-2985	257	1	suppose	suppose	VERB
ejpam-2985	257	2	the	the	DET
ejpam-2985	257	3	mapping	mapping	NOUN
ejpam-2985	257	4	s	s	VERB
ejpam-2985	257	5	:	:	PUNCT
ejpam-2985	257	6	x	x	SYM
ejpam-2985	257	7	→	→	PUNCT
ejpam-2985	257	8	x	x	PUNCT
ejpam-2985	257	9	satisfy	satisfy	VERB
ejpam-2985	257	10	the	the	DET
ejpam-2985	257	11	following	following	NOUN
ejpam-2985	257	12	:	:	PUNCT
ejpam-2985	257	13	d(sx	d(sx	NOUN
ejpam-2985	257	14	,	,	PUNCT
ejpam-2985	257	15	sy	sy	NOUN
ejpam-2985	257	16	)	)	PUNCT
ejpam-2985	257	17	≤	≤	NOUN
ejpam-2985	257	18	ϕ	ϕ	X
ejpam-2985	257	19	(	(	PUNCT
ejpam-2985	257	20	d(x	d(x	PROPN
ejpam-2985	257	21	,	,	PUNCT
ejpam-2985	257	22	y	y	NOUN
ejpam-2985	257	23	)	)	PUNCT
ejpam-2985	257	24	)	)	PUNCT
ejpam-2985	257	25	,	,	PUNCT
ejpam-2985	257	26	for	for	ADP
ejpam-2985	257	27	all	all	DET
ejpam-2985	257	28	x	x	NOUN
ejpam-2985	257	29	,	,	PUNCT
ejpam-2985	257	30	y	y	PROPN
ejpam-2985	257	31	∈	∈	PROPN
ejpam-2985	257	32	x	x	NOUN
ejpam-2985	257	33	,	,	PUNCT
ejpam-2985	257	34	where	where	SCONJ
ejpam-2985	257	35	ϕ	ϕ	PROPN
ejpam-2985	257	36	∈	∈	PROPN
ejpam-2985	257	37	φ	φ	PROPN
ejpam-2985	257	38	.	.	PUNCT
ejpam-2985	258	1	then	then	ADV
ejpam-2985	258	2	s	s	AUX
ejpam-2985	258	3	has	have	VERB
ejpam-2985	258	4	a	a	DET
ejpam-2985	258	5	unique	unique	ADJ
ejpam-2985	258	6	fixed	fix	VERB
ejpam-2985	258	7	point	point	NOUN
ejpam-2985	258	8	in	in	ADP
ejpam-2985	258	9	x.	x.	NOUN
ejpam-2985	258	10	proof	proof	NOUN
ejpam-2985	258	11	.	.	PUNCT
ejpam-2985	259	1	putting	put	VERB
ejpam-2985	259	2	g	g	NOUN
ejpam-2985	259	3	=	=	PUNCT
ejpam-2985	259	4	i	i	PRON
ejpam-2985	259	5	in	in	ADP
ejpam-2985	259	6	corollary	corollary	ADJ
ejpam-2985	259	7	2	2	NUM
ejpam-2985	259	8	,	,	PUNCT
ejpam-2985	259	9	where	where	SCONJ
ejpam-2985	259	10	i	i	PRON
ejpam-2985	259	11	is	be	AUX
ejpam-2985	259	12	the	the	DET
ejpam-2985	259	13	identity	identity	NOUN
ejpam-2985	259	14	mapping	mapping	NOUN
ejpam-2985	259	15	.	.	PUNCT
ejpam-2985	260	1	this	this	PRON
ejpam-2985	260	2	completes	complete	VERB
ejpam-2985	260	3	the	the	DET
ejpam-2985	260	4	proof	proof	NOUN
ejpam-2985	260	5	.	.	PUNCT
ejpam-2985	261	1	corollary	corollary	ADJ
ejpam-2985	261	2	7	7	NUM
ejpam-2985	261	3	.	.	PUNCT
ejpam-2985	261	4	(	(	PUNCT
ejpam-2985	261	5	see	see	VERB
ejpam-2985	261	6	[	[	X
ejpam-2985	261	7	17	17	NUM
ejpam-2985	261	8	]	]	PUNCT
ejpam-2985	261	9	)	)	PUNCT
ejpam-2985	261	10	let	let	VERB
ejpam-2985	261	11	(	(	PUNCT
ejpam-2985	261	12	x	x	NOUN
ejpam-2985	261	13	,	,	PUNCT
ejpam-2985	261	14	d	d	NOUN
ejpam-2985	261	15	)	)	PUNCT
ejpam-2985	261	16	be	be	AUX
ejpam-2985	261	17	a	a	DET
ejpam-2985	261	18	cone	cone	NOUN
ejpam-2985	261	19	rectangular	rectangular	ADJ
ejpam-2985	261	20	metric	metric	ADJ
ejpam-2985	261	21	space	space	NOUN
ejpam-2985	261	22	.	.	PUNCT
ejpam-2985	262	1	suppose	suppose	VERB
ejpam-2985	262	2	the	the	DET
ejpam-2985	262	3	mapping	mapping	NOUN
ejpam-2985	262	4	s	s	VERB
ejpam-2985	262	5	:	:	PUNCT
ejpam-2985	262	6	x	x	SYM
ejpam-2985	262	7	→	→	PUNCT
ejpam-2985	262	8	x	x	PUNCT
ejpam-2985	262	9	satisfy	satisfy	VERB
ejpam-2985	262	10	the	the	DET
ejpam-2985	262	11	following	following	NOUN
ejpam-2985	262	12	:	:	PUNCT
ejpam-2985	262	13	d(sx	d(sx	NOUN
ejpam-2985	262	14	,	,	PUNCT
ejpam-2985	262	15	sy	sy	NOUN
ejpam-2985	262	16	)	)	PUNCT
ejpam-2985	262	17	≤	≤	NOUN
ejpam-2985	262	18	ϕ	ϕ	X
ejpam-2985	262	19	(	(	PUNCT
ejpam-2985	262	20	d(x	d(x	PROPN
ejpam-2985	262	21	,	,	PUNCT
ejpam-2985	262	22	y	y	NOUN
ejpam-2985	262	23	)	)	PUNCT
ejpam-2985	262	24	)	)	PUNCT
ejpam-2985	262	25	,	,	PUNCT
ejpam-2985	262	26	for	for	ADP
ejpam-2985	262	27	all	all	DET
ejpam-2985	262	28	x	x	NOUN
ejpam-2985	262	29	,	,	PUNCT
ejpam-2985	262	30	y	y	PROPN
ejpam-2985	262	31	∈	∈	PROPN
ejpam-2985	262	32	x	x	NOUN
ejpam-2985	262	33	,	,	PUNCT
ejpam-2985	262	34	where	where	SCONJ
ejpam-2985	262	35	ϕ	ϕ	PROPN
ejpam-2985	262	36	∈	∈	PROPN
ejpam-2985	262	37	φ	φ	PROPN
ejpam-2985	262	38	.	.	PUNCT
ejpam-2985	263	1	then	then	ADV
ejpam-2985	263	2	s	s	AUX
ejpam-2985	263	3	has	have	VERB
ejpam-2985	263	4	a	a	DET
ejpam-2985	263	5	unique	unique	ADJ
ejpam-2985	263	6	fixed	fix	VERB
ejpam-2985	263	7	point	point	NOUN
ejpam-2985	263	8	in	in	ADP
ejpam-2985	263	9	x.	x.	NOUN
ejpam-2985	263	10	proof	proof	NOUN
ejpam-2985	263	11	.	.	PUNCT
ejpam-2985	264	1	this	this	PRON
ejpam-2985	264	2	follows	follow	VERB
ejpam-2985	264	3	from	from	ADP
ejpam-2985	264	4	the	the	DET
ejpam-2985	264	5	remark	remark	NOUN
ejpam-2985	264	6	2	2	NUM
ejpam-2985	264	7	and	and	CCONJ
ejpam-2985	264	8	putting	put	VERB
ejpam-2985	264	9	g	g	NOUN
ejpam-2985	264	10	=	=	PUNCT
ejpam-2985	264	11	i	i	PRON
ejpam-2985	264	12	in	in	ADP
ejpam-2985	264	13	corollary	corollary	ADJ
ejpam-2985	264	14	2	2	NUM
ejpam-2985	264	15	.	.	PUNCT
ejpam-2985	264	16	corollary	corollary	ADJ
ejpam-2985	264	17	8	8	NUM
ejpam-2985	264	18	.	.	PUNCT
ejpam-2985	265	1	(	(	PUNCT
ejpam-2985	265	2	see	see	VERB
ejpam-2985	265	3	[	[	X
ejpam-2985	265	4	9	9	NUM
ejpam-2985	265	5	]	]	PUNCT
ejpam-2985	265	6	)	)	PUNCT
ejpam-2985	265	7	let	let	VERB
ejpam-2985	265	8	(	(	PUNCT
ejpam-2985	265	9	x	x	NOUN
ejpam-2985	265	10	,	,	PUNCT
ejpam-2985	265	11	d	d	NOUN
ejpam-2985	265	12	)	)	PUNCT
ejpam-2985	265	13	be	be	AUX
ejpam-2985	265	14	a	a	DET
ejpam-2985	265	15	cone	cone	NOUN
ejpam-2985	265	16	pentagonal	pentagonal	ADJ
ejpam-2985	265	17	metric	metric	ADJ
ejpam-2985	265	18	space	space	NOUN
ejpam-2985	265	19	and	and	CCONJ
ejpam-2985	265	20	p	p	NOUN
ejpam-2985	265	21	be	be	AUX
ejpam-2985	265	22	a	a	DET
ejpam-2985	265	23	normal	normal	ADJ
ejpam-2985	265	24	cone	cone	NOUN
ejpam-2985	265	25	with	with	ADP
ejpam-2985	265	26	normal	normal	ADJ
ejpam-2985	265	27	constant	constant	ADJ
ejpam-2985	265	28	k.	k.	PROPN
ejpam-2985	265	29	suppose	suppose	VERB
ejpam-2985	265	30	the	the	DET
ejpam-2985	265	31	mapping	mapping	NOUN
ejpam-2985	265	32	s	s	VERB
ejpam-2985	265	33	:	:	PUNCT
ejpam-2985	265	34	x	x	SYM
ejpam-2985	265	35	→	→	SYM
ejpam-2985	265	36	x	x	SYM
ejpam-2985	265	37	satisfies	satisfy	VERB
ejpam-2985	265	38	the	the	DET
ejpam-2985	265	39	contractive	contractive	ADJ
ejpam-2985	265	40	condition	condition	NOUN
ejpam-2985	265	41	:	:	PUNCT
ejpam-2985	265	42	d(sx	d(sx	NOUN
ejpam-2985	265	43	,	,	PUNCT
ejpam-2985	265	44	sy	sy	NOUN
ejpam-2985	265	45	)	)	PUNCT
ejpam-2985	265	46	≤	≤	NOUN
ejpam-2985	265	47	λd(x	λd(x	PUNCT
ejpam-2985	265	48	,	,	PUNCT
ejpam-2985	265	49	y	y	NOUN
ejpam-2985	265	50	)	)	PUNCT
ejpam-2985	265	51	,	,	PUNCT
ejpam-2985	265	52	for	for	ADP
ejpam-2985	265	53	all	all	DET
ejpam-2985	265	54	x	x	NOUN
ejpam-2985	265	55	,	,	PUNCT
ejpam-2985	265	56	y	y	PROPN
ejpam-2985	265	57	∈	∈	PROPN
ejpam-2985	265	58	x	x	NOUN
ejpam-2985	265	59	,	,	PUNCT
ejpam-2985	265	60	where	where	SCONJ
ejpam-2985	265	61	λ	λ	PROPN
ejpam-2985	265	62	∈	∈	PROPN
ejpam-2985	266	1	[	[	X
ejpam-2985	266	2	0	0	NUM
ejpam-2985	266	3	,	,	PUNCT
ejpam-2985	266	4	1	1	NUM
ejpam-2985	266	5	)	)	PUNCT
ejpam-2985	266	6	.	.	PUNCT
ejpam-2985	267	1	then	then	ADV
ejpam-2985	267	2	s	s	AUX
ejpam-2985	267	3	has	have	VERB
ejpam-2985	267	4	a	a	DET
ejpam-2985	267	5	unique	unique	ADJ
ejpam-2985	267	6	fixed	fix	VERB
ejpam-2985	267	7	point	point	NOUN
ejpam-2985	267	8	in	in	ADP
ejpam-2985	267	9	x.	x.	NOUN
ejpam-2985	267	10	proof	proof	NOUN
ejpam-2985	267	11	.	.	PUNCT
ejpam-2985	268	1	putting	put	VERB
ejpam-2985	268	2	g	g	NOUN
ejpam-2985	268	3	=	=	PUNCT
ejpam-2985	268	4	i	i	PRON
ejpam-2985	268	5	in	in	ADP
ejpam-2985	268	6	corollary	corollary	ADJ
ejpam-2985	268	7	3	3	NUM
ejpam-2985	268	8	,	,	PUNCT
ejpam-2985	268	9	where	where	SCONJ
ejpam-2985	268	10	i	i	PRON
ejpam-2985	268	11	is	be	AUX
ejpam-2985	268	12	the	the	DET
ejpam-2985	268	13	identity	identity	NOUN
ejpam-2985	268	14	mapping	mapping	NOUN
ejpam-2985	268	15	.	.	PUNCT
ejpam-2985	269	1	this	this	PRON
ejpam-2985	269	2	completes	complete	VERB
ejpam-2985	269	3	the	the	DET
ejpam-2985	269	4	proof	proof	NOUN
ejpam-2985	269	5	.	.	PUNCT
ejpam-2985	270	1	corollary	corollary	ADJ
ejpam-2985	270	2	9	9	NUM
ejpam-2985	270	3	.	.	PUNCT
ejpam-2985	271	1	(	(	PUNCT
ejpam-2985	271	2	see	see	VERB
ejpam-2985	271	3	[	[	X
ejpam-2985	271	4	6	6	NUM
ejpam-2985	271	5	]	]	PUNCT
ejpam-2985	271	6	)	)	PUNCT
ejpam-2985	271	7	let	let	VERB
ejpam-2985	271	8	(	(	PUNCT
ejpam-2985	271	9	x	x	NOUN
ejpam-2985	271	10	,	,	PUNCT
ejpam-2985	271	11	d	d	NOUN
ejpam-2985	271	12	)	)	PUNCT
ejpam-2985	271	13	be	be	AUX
ejpam-2985	271	14	a	a	DET
ejpam-2985	271	15	cone	cone	NOUN
ejpam-2985	271	16	rectangular	rectangular	ADJ
ejpam-2985	271	17	metric	metric	ADJ
ejpam-2985	271	18	space	space	NOUN
ejpam-2985	271	19	and	and	CCONJ
ejpam-2985	271	20	p	p	NOUN
ejpam-2985	271	21	be	be	AUX
ejpam-2985	271	22	a	a	DET
ejpam-2985	271	23	normal	normal	ADJ
ejpam-2985	271	24	cone	cone	NOUN
ejpam-2985	271	25	with	with	ADP
ejpam-2985	271	26	normal	normal	ADJ
ejpam-2985	271	27	constant	constant	ADJ
ejpam-2985	271	28	k.	k.	PROPN
ejpam-2985	271	29	suppose	suppose	VERB
ejpam-2985	271	30	the	the	DET
ejpam-2985	271	31	mapping	mapping	NOUN
ejpam-2985	271	32	s	s	VERB
ejpam-2985	271	33	:	:	PUNCT
ejpam-2985	271	34	x	x	SYM
ejpam-2985	271	35	→	→	SYM
ejpam-2985	271	36	x	x	NOUN
ejpam-2985	271	37	satisfies	satisfie	NOUN
ejpam-2985	271	38	:	:	PUNCT
ejpam-2985	271	39	d(sx	d(sx	NOUN
ejpam-2985	271	40	,	,	PUNCT
ejpam-2985	271	41	sy	sy	NOUN
ejpam-2985	271	42	)	)	PUNCT
ejpam-2985	271	43	≤	≤	NOUN
ejpam-2985	271	44	λd(x	λd(x	PUNCT
ejpam-2985	271	45	,	,	PUNCT
ejpam-2985	271	46	y	y	NOUN
ejpam-2985	271	47	)	)	PUNCT
ejpam-2985	271	48	,	,	PUNCT
ejpam-2985	271	49	for	for	ADP
ejpam-2985	271	50	all	all	DET
ejpam-2985	271	51	x	x	NOUN
ejpam-2985	271	52	,	,	PUNCT
ejpam-2985	271	53	y	y	PROPN
ejpam-2985	271	54	∈	∈	PROPN
ejpam-2985	271	55	x	x	NOUN
ejpam-2985	271	56	,	,	PUNCT
ejpam-2985	271	57	where	where	SCONJ
ejpam-2985	271	58	λ	λ	PROPN
ejpam-2985	271	59	∈	∈	PROPN
ejpam-2985	272	1	[	[	X
ejpam-2985	272	2	0	0	NUM
ejpam-2985	272	3	,	,	PUNCT
ejpam-2985	272	4	1	1	NUM
ejpam-2985	272	5	)	)	PUNCT
ejpam-2985	272	6	.	.	PUNCT
ejpam-2985	273	1	then	then	ADV
ejpam-2985	273	2	s	s	AUX
ejpam-2985	273	3	has	have	VERB
ejpam-2985	273	4	a	a	DET
ejpam-2985	273	5	unique	unique	ADJ
ejpam-2985	273	6	fixed	fix	VERB
ejpam-2985	273	7	point	point	NOUN
ejpam-2985	273	8	in	in	ADP
ejpam-2985	273	9	x.	x.	NOUN
ejpam-2985	273	10	proof	proof	NOUN
ejpam-2985	273	11	.	.	PUNCT
ejpam-2985	274	1	putting	put	VERB
ejpam-2985	274	2	g	g	NOUN
ejpam-2985	274	3	=	=	PUNCT
ejpam-2985	274	4	i	i	PRON
ejpam-2985	274	5	in	in	ADP
ejpam-2985	274	6	corollary	corollary	ADJ
ejpam-2985	274	7	3	3	NUM
ejpam-2985	274	8	and	and	CCONJ
ejpam-2985	274	9	remark	remark	NOUN
ejpam-2985	274	10	2	2	NUM
ejpam-2985	274	11	,	,	PUNCT
ejpam-2985	274	12	the	the	DET
ejpam-2985	274	13	results	result	NOUN
ejpam-2985	274	14	follows	follow	VERB
ejpam-2985	274	15	.	.	PUNCT
ejpam-2985	275	1	theorem	theorem	NOUN
ejpam-2985	275	2	2	2	NUM
ejpam-2985	275	3	.	.	X
ejpam-2985	276	1	let	let	VERB
ejpam-2985	276	2	(	(	PUNCT
ejpam-2985	276	3	x	x	NOUN
ejpam-2985	276	4	,	,	PUNCT
ejpam-2985	276	5	d	d	NOUN
ejpam-2985	276	6	)	)	PUNCT
ejpam-2985	276	7	be	be	AUX
ejpam-2985	276	8	a	a	DET
ejpam-2985	276	9	cone	cone	NOUN
ejpam-2985	276	10	pentagonal	pentagonal	ADJ
ejpam-2985	276	11	metric	metric	ADJ
ejpam-2985	276	12	space	space	NOUN
ejpam-2985	276	13	.	.	PUNCT
ejpam-2985	277	1	suppose	suppose	VERB
ejpam-2985	277	2	the	the	DET
ejpam-2985	277	3	mappings	mapping	NOUN
ejpam-2985	277	4	s	s	PART
ejpam-2985	277	5	,	,	PUNCT
ejpam-2985	277	6	f	f	PROPN
ejpam-2985	277	7	,	,	PUNCT
ejpam-2985	277	8	g	g	NOUN
ejpam-2985	277	9	:	:	PUNCT
ejpam-2985	277	10	x	x	SYM
ejpam-2985	277	11	→	→	PUNCT
ejpam-2985	277	12	x	x	SYM
ejpam-2985	277	13	satisfies	satisfy	VERB
ejpam-2985	277	14	the	the	DET
ejpam-2985	277	15	contractive	contractive	ADJ
ejpam-2985	277	16	condition	condition	NOUN
ejpam-2985	277	17	:	:	PUNCT
ejpam-2985	277	18	d(sx	d(sx	PROPN
ejpam-2985	277	19	,	,	PUNCT
ejpam-2985	277	20	fy	fy	NOUN
ejpam-2985	277	21	)	)	PUNCT
ejpam-2985	277	22	≤	≤	NOUN
ejpam-2985	278	1	λ	λ	PROPN
ejpam-2985	278	2	[	[	PUNCT
ejpam-2985	278	3	d(gx	d(gx	PROPN
ejpam-2985	278	4	,	,	PUNCT
ejpam-2985	278	5	sx	sx	PROPN
ejpam-2985	278	6	)	)	PUNCT
ejpam-2985	278	7	+	+	NUM
ejpam-2985	278	8	d(gy	d(gy	PROPN
ejpam-2985	278	9	,	,	PUNCT
ejpam-2985	278	10	fy	fy	PROPN
ejpam-2985	278	11	)	)	PUNCT
ejpam-2985	278	12	]	]	PUNCT
ejpam-2985	278	13	,	,	PUNCT
ejpam-2985	278	14	(	(	PUNCT
ejpam-2985	278	15	19	19	NUM
ejpam-2985	278	16	)	)	PUNCT
ejpam-2985	278	17	for	for	ADP
ejpam-2985	278	18	all	all	DET
ejpam-2985	278	19	x	x	NOUN
ejpam-2985	278	20	,	,	PUNCT
ejpam-2985	278	21	y	y	PROPN
ejpam-2985	278	22	∈	∈	PROPN
ejpam-2985	278	23	x	x	NOUN
ejpam-2985	278	24	,	,	PUNCT
ejpam-2985	278	25	where	where	SCONJ
ejpam-2985	278	26	λ	λ	PROPN
ejpam-2985	278	27	∈	∈	PROPN
ejpam-2985	279	1	[	[	X
ejpam-2985	279	2	0	0	NUM
ejpam-2985	279	3	,	,	PUNCT
ejpam-2985	279	4	1/2	1/2	NUM
ejpam-2985	279	5	)	)	PUNCT
ejpam-2985	279	6	.	.	PUNCT
ejpam-2985	280	1	suppose	suppose	VERB
ejpam-2985	280	2	that	that	SCONJ
ejpam-2985	280	3	s(x	s(x	NOUN
ejpam-2985	280	4	)	)	PUNCT
ejpam-2985	280	5	∪	∪	ADP
ejpam-2985	280	6	f(x	f(x	PROPN
ejpam-2985	280	7	)	)	PUNCT
ejpam-2985	280	8	⊆	⊆	NUM
ejpam-2985	280	9	g(x	g(x	NOUN
ejpam-2985	280	10	)	)	PUNCT
ejpam-2985	280	11	,	,	PUNCT
ejpam-2985	280	12	and	and	CCONJ
ejpam-2985	280	13	g(x	g(x	NOUN
ejpam-2985	280	14	)	)	PUNCT
ejpam-2985	280	15	is	be	AUX
ejpam-2985	280	16	a	a	DET
ejpam-2985	280	17	complete	complete	ADJ
ejpam-2985	280	18	subspace	subspace	NOUN
ejpam-2985	280	19	of	of	ADP
ejpam-2985	280	20	x	x	PRON
ejpam-2985	280	21	,	,	PUNCT
ejpam-2985	280	22	then	then	ADV
ejpam-2985	280	23	the	the	DET
ejpam-2985	280	24	mappings	mapping	NOUN
ejpam-2985	280	25	s	s	PART
ejpam-2985	280	26	,	,	PUNCT
ejpam-2985	280	27	f	f	PROPN
ejpam-2985	280	28	and	and	CCONJ
ejpam-2985	280	29	g	g	PROPN
ejpam-2985	280	30	have	have	VERB
ejpam-2985	280	31	a	a	DET
ejpam-2985	280	32	unique	unique	ADJ
ejpam-2985	280	33	point	point	NOUN
ejpam-2985	280	34	of	of	ADP
ejpam-2985	280	35	coincidence	coincidence	NOUN
ejpam-2985	280	36	in	in	ADP
ejpam-2985	280	37	x.	x.	NOUN
ejpam-2985	280	38	moreover	moreover	ADV
ejpam-2985	280	39	,	,	PUNCT
ejpam-2985	280	40	if	if	SCONJ
ejpam-2985	280	41	(	(	PUNCT
ejpam-2985	280	42	s	s	X
ejpam-2985	280	43	,	,	PUNCT
ejpam-2985	280	44	g	g	NOUN
ejpam-2985	280	45	)	)	PUNCT
ejpam-2985	280	46	and	and	CCONJ
ejpam-2985	280	47	(	(	PUNCT
ejpam-2985	280	48	f	f	X
ejpam-2985	280	49	,	,	PUNCT
ejpam-2985	280	50	g	g	NOUN
ejpam-2985	280	51	)	)	PUNCT
ejpam-2985	280	52	are	be	AUX
ejpam-2985	280	53	weakly	weakly	ADV
ejpam-2985	280	54	compatible	compatible	ADJ
ejpam-2985	280	55	then	then	ADV
ejpam-2985	280	56	s	s	PROPN
ejpam-2985	280	57	,	,	PUNCT
ejpam-2985	280	58	f	f	PROPN
ejpam-2985	280	59	and	and	CCONJ
ejpam-2985	280	60	g	g	PROPN
ejpam-2985	280	61	have	have	VERB
ejpam-2985	280	62	a	a	DET
ejpam-2985	280	63	unique	unique	ADJ
ejpam-2985	280	64	common	common	ADJ
ejpam-2985	280	65	fixed	fix	VERB
ejpam-2985	280	66	point	point	NOUN
ejpam-2985	280	67	in	in	ADP
ejpam-2985	280	68	x.	x.	PROPN
ejpam-2985	280	69	a.	a.	PROPN
ejpam-2985	280	70	auwalu	auwalu	PROPN
ejpam-2985	280	71	,	,	PUNCT
ejpam-2985	280	72	e.	e.	PROPN
ejpam-2985	280	73	hınçal	hınçal	PROPN
ejpam-2985	280	74	/	/	SYM
ejpam-2985	280	75	eur	eur	PROPN
ejpam-2985	280	76	.	.	PUNCT
ejpam-2985	281	1	j.	j.	PROPN
ejpam-2985	281	2	pure	pure	PROPN
ejpam-2985	281	3	appl	appl	PROPN
ejpam-2985	281	4	.	.	PROPN
ejpam-2985	281	5	math	math	PROPN
ejpam-2985	281	6	,	,	PUNCT
ejpam-2985	281	7	10	10	NUM
ejpam-2985	281	8	(	(	PUNCT
ejpam-2985	281	9	3	3	NUM
ejpam-2985	281	10	)	)	PUNCT
ejpam-2985	281	11	(	(	PUNCT
ejpam-2985	281	12	2017	2017	NUM
ejpam-2985	281	13	)	)	PUNCT
ejpam-2985	281	14	,	,	PUNCT
ejpam-2985	281	15	473	473	NUM
ejpam-2985	281	16	-	-	SYM
ejpam-2985	281	17	487	487	NUM
ejpam-2985	281	18	483	483	NUM
ejpam-2985	281	19	proof	proof	NOUN
ejpam-2985	281	20	.	.	PUNCT
ejpam-2985	282	1	let	let	VERB
ejpam-2985	282	2	x0	x0	PROPN
ejpam-2985	282	3	be	be	AUX
ejpam-2985	282	4	an	an	DET
ejpam-2985	282	5	arbitrary	arbitrary	ADJ
ejpam-2985	282	6	point	point	NOUN
ejpam-2985	282	7	in	in	ADP
ejpam-2985	282	8	x.	x.	NOUN
ejpam-2985	282	9	define	define	NOUN
ejpam-2985	282	10	,	,	PUNCT
ejpam-2985	282	11	like	like	ADP
ejpam-2985	282	12	in	in	ADP
ejpam-2985	282	13	theorem	theorem	NOUN
ejpam-2985	282	14	1	1	NUM
ejpam-2985	282	15	,	,	PUNCT
ejpam-2985	282	16	a	a	DET
ejpam-2985	282	17	sequence	sequence	NOUN
ejpam-2985	282	18	{	{	PUNCT
ejpam-2985	282	19	gxn	gxn	INTJ
ejpam-2985	282	20	}	}	PUNCT
ejpam-2985	282	21	in	in	ADP
ejpam-2985	282	22	x	x	X
ejpam-2985	282	23	such	such	ADJ
ejpam-2985	282	24	that	that	DET
ejpam-2985	282	25	gxn+1	gxn+1	PROPN
ejpam-2985	282	26	=	=	SYM
ejpam-2985	282	27	sxn	sxn	NOUN
ejpam-2985	282	28	and	and	CCONJ
ejpam-2985	282	29	gxn+2	gxn+2	X
ejpam-2985	282	30	=	=	SYM
ejpam-2985	282	31	fxn+1	fxn+1	PROPN
ejpam-2985	282	32	,	,	PUNCT
ejpam-2985	282	33	for	for	ADP
ejpam-2985	282	34	all	all	DET
ejpam-2985	282	35	n	n	NOUN
ejpam-2985	282	36	=	=	SYM
ejpam-2985	282	37	0	0	NUM
ejpam-2985	282	38	,	,	PUNCT
ejpam-2985	282	39	1	1	NUM
ejpam-2985	282	40	,	,	PUNCT
ejpam-2985	282	41	2	2	NUM
ejpam-2985	282	42	,	,	PUNCT
ejpam-2985	282	43	·	·	PUNCT
ejpam-2985	282	44	·	·	PUNCT
ejpam-2985	282	45	·	·	PUNCT
ejpam-2985	282	46	.	.	PUNCT
ejpam-2985	283	1	we	we	PRON
ejpam-2985	283	2	assume	assume	VERB
ejpam-2985	283	3	that	that	SCONJ
ejpam-2985	283	4	xn	xn	PROPN
ejpam-2985	284	1	6=	6=	NUM
ejpam-2985	284	2	xn+1	xn+1	PROPN
ejpam-2985	284	3	,	,	PUNCT
ejpam-2985	284	4	for	for	ADP
ejpam-2985	284	5	all	all	DET
ejpam-2985	284	6	n	n	PRON
ejpam-2985	284	7	∈	∈	PROPN
ejpam-2985	284	8	n.	n.	NOUN
ejpam-2985	284	9	then	then	ADV
ejpam-2985	284	10	,	,	PUNCT
ejpam-2985	284	11	from	from	ADP
ejpam-2985	284	12	(	(	PUNCT
ejpam-2985	284	13	19	19	NUM
ejpam-2985	284	14	)	)	PUNCT
ejpam-2985	284	15	,	,	PUNCT
ejpam-2985	284	16	it	it	PRON
ejpam-2985	284	17	follows	follow	VERB
ejpam-2985	284	18	that	that	SCONJ
ejpam-2985	284	19	d(gxn	d(gxn	VERB
ejpam-2985	284	20	,	,	PUNCT
ejpam-2985	284	21	gxn+1	gxn+1	NOUN
ejpam-2985	284	22	)	)	PUNCT
ejpam-2985	285	1	=	=	SYM
ejpam-2985	285	2	d(sxn−1	d(sxn−1	PROPN
ejpam-2985	285	3	,	,	PUNCT
ejpam-2985	285	4	fxn	fxn	NOUN
ejpam-2985	285	5	)	)	PUNCT
ejpam-2985	285	6	≤	≤	NOUN
ejpam-2985	285	7	λ	λ	PROPN
ejpam-2985	285	8	(	(	PUNCT
ejpam-2985	285	9	d(gxn−1	d(gxn−1	PROPN
ejpam-2985	285	10	,	,	PUNCT
ejpam-2985	285	11	sxn−1	sxn−1	PROPN
ejpam-2985	285	12	)	)	PUNCT
ejpam-2985	285	13	+	+	CCONJ
ejpam-2985	285	14	d(gxn	d(gxn	PROPN
ejpam-2985	285	15	,	,	PUNCT
ejpam-2985	285	16	fxn	fxn	NOUN
ejpam-2985	285	17	)	)	PUNCT
ejpam-2985	285	18	)	)	PUNCT
ejpam-2985	286	1	≤	≤	NUM
ejpam-2985	286	2	λ	λ	PROPN
ejpam-2985	286	3	(	(	PUNCT
ejpam-2985	286	4	d(gxn−1	d(gxn−1	PROPN
ejpam-2985	286	5	,	,	PUNCT
ejpam-2985	286	6	gxn	gxn	PROPN
ejpam-2985	286	7	)	)	PUNCT
ejpam-2985	286	8	+	+	CCONJ
ejpam-2985	286	9	d(gxn	d(gxn	PROPN
ejpam-2985	286	10	,	,	PUNCT
ejpam-2985	286	11	gxn+1	gxn+1	PROPN
ejpam-2985	286	12	)	)	PUNCT
ejpam-2985	286	13	)	)	PUNCT
ejpam-2985	286	14	.	.	PUNCT
ejpam-2985	287	1	so	so	ADV
ejpam-2985	287	2	that	that	SCONJ
ejpam-2985	287	3	,	,	PUNCT
ejpam-2985	287	4	d(gxn	d(gxn	PROPN
ejpam-2985	287	5	,	,	PUNCT
ejpam-2985	287	6	gxn+1	gxn+1	NOUN
ejpam-2985	287	7	)	)	PUNCT
ejpam-2985	287	8	≤	≤	NUM
ejpam-2985	287	9	λ	λ	PROPN
ejpam-2985	287	10	1−	1−	NUM
ejpam-2985	287	11	λ	λ	SYM
ejpam-2985	287	12	d(gxn−1	d(gxn−1	PROPN
ejpam-2985	287	13	,	,	PUNCT
ejpam-2985	287	14	gxn	gxn	PROPN
ejpam-2985	287	15	)	)	PUNCT
ejpam-2985	287	16	≤	≤	NOUN
ejpam-2985	288	1	rd(gxn−1	rd(gxn−1	ADJ
ejpam-2985	288	2	,	,	PUNCT
ejpam-2985	288	3	gxn	gxn	PROPN
ejpam-2985	288	4	)	)	PUNCT
ejpam-2985	288	5	,	,	PUNCT
ejpam-2985	288	6	where	where	SCONJ
ejpam-2985	288	7	r	r	NOUN
ejpam-2985	288	8	=	=	SYM
ejpam-2985	288	9	λ	λ	X
ejpam-2985	288	10	1−	1−	NUM
ejpam-2985	288	11	λ	λ	X
ejpam-2985	288	12	∈	∈	PROPN
ejpam-2985	288	13	[	[	X
ejpam-2985	288	14	0	0	NUM
ejpam-2985	288	15	,	,	PUNCT
ejpam-2985	288	16	1	1	NUM
ejpam-2985	288	17	)	)	PUNCT
ejpam-2985	288	18	≤	≤	NUM
ejpam-2985	288	19	r2d(gxn−2	r2d(gxn−2	PROPN
ejpam-2985	288	20	,	,	PUNCT
ejpam-2985	288	21	gxn−1	gxn−1	PROPN
ejpam-2985	288	22	)	)	PUNCT
ejpam-2985	288	23	...	...	PUNCT
ejpam-2985	289	1	≤	≤	PROPN
ejpam-2985	289	2	rn	rn	PROPN
ejpam-2985	289	3	(	(	PUNCT
ejpam-2985	289	4	d(gx0	d(gx0	PROPN
ejpam-2985	289	5	,	,	PUNCT
ejpam-2985	289	6	gx1	gx1	PROPN
ejpam-2985	289	7	)	)	PUNCT
ejpam-2985	289	8	)	)	PUNCT
ejpam-2985	289	9	.	.	PUNCT
ejpam-2985	290	1	(	(	PUNCT
ejpam-2985	290	2	20	20	NUM
ejpam-2985	290	3	)	)	PUNCT
ejpam-2985	290	4	in	in	ADP
ejpam-2985	290	5	similar	similar	ADJ
ejpam-2985	290	6	way	way	NOUN
ejpam-2985	290	7	,	,	PUNCT
ejpam-2985	290	8	it	it	PRON
ejpam-2985	290	9	again	again	ADV
ejpam-2985	290	10	follows	follow	VERB
ejpam-2985	290	11	that	that	PRON
ejpam-2985	290	12	d(gxn	d(gxn	VERB
ejpam-2985	290	13	,	,	PUNCT
ejpam-2985	290	14	gxn+2	gxn+2	PROPN
ejpam-2985	290	15	)	)	PUNCT
ejpam-2985	290	16	≤	≤	PROPN
ejpam-2985	291	1	rn	rn	PROPN
ejpam-2985	291	2	(	(	PUNCT
ejpam-2985	291	3	d(gx0	d(gx0	PROPN
ejpam-2985	291	4	,	,	PUNCT
ejpam-2985	291	5	gx2	gx2	PROPN
ejpam-2985	291	6	)	)	PUNCT
ejpam-2985	291	7	)	)	PUNCT
ejpam-2985	291	8	,	,	PUNCT
ejpam-2985	291	9	(	(	PUNCT
ejpam-2985	291	10	21	21	NUM
ejpam-2985	291	11	)	)	PUNCT
ejpam-2985	291	12	and	and	CCONJ
ejpam-2985	291	13	d(gxn	d(gxn	VERB
ejpam-2985	291	14	,	,	PUNCT
ejpam-2985	291	15	gxn+3	gxn+3	NOUN
ejpam-2985	291	16	)	)	PUNCT
ejpam-2985	291	17	≤	≤	PROPN
ejpam-2985	292	1	rn	rn	PROPN
ejpam-2985	292	2	(	(	PUNCT
ejpam-2985	292	3	d(gx0	d(gx0	PROPN
ejpam-2985	292	4	,	,	PUNCT
ejpam-2985	292	5	gx3	gx3	NOUN
ejpam-2985	292	6	)	)	PUNCT
ejpam-2985	292	7	)	)	PUNCT
ejpam-2985	292	8	.	.	PUNCT
ejpam-2985	293	1	(	(	PUNCT
ejpam-2985	293	2	22	22	NUM
ejpam-2985	293	3	)	)	PUNCT
ejpam-2985	293	4	similarly	similarly	ADV
ejpam-2985	293	5	,	,	PUNCT
ejpam-2985	293	6	for	for	ADP
ejpam-2985	293	7	k	k	PROPN
ejpam-2985	293	8	=	=	SYM
ejpam-2985	293	9	1	1	NUM
ejpam-2985	293	10	,	,	PUNCT
ejpam-2985	293	11	2	2	NUM
ejpam-2985	293	12	,	,	PUNCT
ejpam-2985	293	13	3	3	NUM
ejpam-2985	293	14	,	,	PUNCT
ejpam-2985	293	15	·	·	PUNCT
ejpam-2985	293	16	·	·	PUNCT
ejpam-2985	293	17	·	·	PUNCT
ejpam-2985	293	18	,	,	PUNCT
ejpam-2985	293	19	it	it	PRON
ejpam-2985	293	20	further	far	ADV
ejpam-2985	293	21	follows	follow	VERB
ejpam-2985	293	22	that	that	SCONJ
ejpam-2985	293	23	d(gxn	d(gxn	VERB
ejpam-2985	293	24	,	,	PUNCT
ejpam-2985	293	25	gxn+3k+1	gxn+3k+1	NOUN
ejpam-2985	293	26	)	)	PUNCT
ejpam-2985	293	27	≤	≤	PROPN
ejpam-2985	294	1	rn	rn	PROPN
ejpam-2985	294	2	(	(	PUNCT
ejpam-2985	294	3	d(gx0	d(gx0	PROPN
ejpam-2985	294	4	,	,	PUNCT
ejpam-2985	294	5	gx3k+1	gx3k+1	PROPN
ejpam-2985	294	6	)	)	PUNCT
ejpam-2985	294	7	)	)	PUNCT
ejpam-2985	294	8	,	,	PUNCT
ejpam-2985	294	9	(	(	PUNCT
ejpam-2985	294	10	23	23	X
ejpam-2985	294	11	)	)	PUNCT
ejpam-2985	294	12	d(gxn	d(gxn	PROPN
ejpam-2985	294	13	,	,	PUNCT
ejpam-2985	294	14	gxn+3k+2	gxn+3k+2	NOUN
ejpam-2985	294	15	)	)	PUNCT
ejpam-2985	294	16	≤	≤	PROPN
ejpam-2985	294	17	rn	rn	PROPN
ejpam-2985	294	18	(	(	PUNCT
ejpam-2985	294	19	d(gx0	d(gx0	PROPN
ejpam-2985	294	20	,	,	PUNCT
ejpam-2985	294	21	gx3k+2	gx3k+2	NOUN
ejpam-2985	294	22	)	)	PUNCT
ejpam-2985	294	23	)	)	PUNCT
ejpam-2985	294	24	,	,	PUNCT
ejpam-2985	294	25	(	(	PUNCT
ejpam-2985	294	26	24	24	NUM
ejpam-2985	294	27	)	)	PUNCT
ejpam-2985	294	28	d(gxn	d(gxn	PROPN
ejpam-2985	294	29	,	,	PUNCT
ejpam-2985	294	30	gxn+3k+3	gxn+3k+3	ADJ
ejpam-2985	294	31	)	)	PUNCT
ejpam-2985	294	32	≤	≤	PROPN
ejpam-2985	294	33	rn	rn	PROPN
ejpam-2985	294	34	(	(	PUNCT
ejpam-2985	294	35	d(gx0	d(gx0	PROPN
ejpam-2985	294	36	,	,	PUNCT
ejpam-2985	294	37	gx3k+3	gx3k+3	PROPN
ejpam-2985	294	38	)	)	PUNCT
ejpam-2985	294	39	)	)	PUNCT
ejpam-2985	294	40	.	.	PUNCT
ejpam-2985	295	1	(	(	PUNCT
ejpam-2985	295	2	25	25	NUM
ejpam-2985	295	3	)	)	PUNCT
ejpam-2985	295	4	using	use	VERB
ejpam-2985	295	5	the	the	DET
ejpam-2985	295	6	same	same	ADJ
ejpam-2985	295	7	argument	argument	NOUN
ejpam-2985	295	8	in	in	ADP
ejpam-2985	295	9	the	the	DET
ejpam-2985	295	10	proof	proof	NOUN
ejpam-2985	295	11	of	of	ADP
ejpam-2985	295	12	theorem	theorem	NOUN
ejpam-2985	295	13	1	1	NUM
ejpam-2985	295	14	,	,	PUNCT
ejpam-2985	295	15	we	we	PRON
ejpam-2985	295	16	can	can	AUX
ejpam-2985	295	17	show	show	VERB
ejpam-2985	295	18	that	that	SCONJ
ejpam-2985	295	19	{	{	PUNCT
ejpam-2985	295	20	gxn	gxn	INTJ
ejpam-2985	295	21	}	}	PUNCT
ejpam-2985	295	22	is	be	AUX
ejpam-2985	295	23	a	a	DET
ejpam-2985	295	24	cauchy	cauchy	ADJ
ejpam-2985	295	25	sequence	sequence	NOUN
ejpam-2985	295	26	in	in	ADP
ejpam-2985	295	27	x.	x.	NOUN
ejpam-2985	295	28	since	since	SCONJ
ejpam-2985	295	29	g(x	g(x	NOUN
ejpam-2985	295	30	)	)	PUNCT
ejpam-2985	295	31	is	be	AUX
ejpam-2985	295	32	a	a	DET
ejpam-2985	295	33	complete	complete	ADJ
ejpam-2985	295	34	subspace	subspace	NOUN
ejpam-2985	295	35	of	of	ADP
ejpam-2985	295	36	x	x	PRON
ejpam-2985	295	37	,	,	PUNCT
ejpam-2985	295	38	there	there	PRON
ejpam-2985	295	39	exists	exist	VERB
ejpam-2985	295	40	a	a	DET
ejpam-2985	295	41	points	point	NOUN
ejpam-2985	295	42	u	u	NOUN
ejpam-2985	295	43	,	,	PUNCT
ejpam-2985	295	44	v	v	NOUN
ejpam-2985	295	45	∈	∈	PROPN
ejpam-2985	295	46	g(x	g(x	NOUN
ejpam-2985	295	47	)	)	PUNCT
ejpam-2985	295	48	such	such	ADJ
ejpam-2985	295	49	that	that	SCONJ
ejpam-2985	295	50	limn→∞	limn→∞	PROPN
ejpam-2985	295	51	gxn	gxn	NOUN
ejpam-2985	295	52	=	=	SYM
ejpam-2985	295	53	v	v	NOUN
ejpam-2985	295	54	=	=	SYM
ejpam-2985	295	55	gu	gu	NOUN
ejpam-2985	295	56	.	.	PUNCT
ejpam-2985	296	1	now	now	ADV
ejpam-2985	296	2	,	,	PUNCT
ejpam-2985	296	3	we	we	PRON
ejpam-2985	296	4	show	show	VERB
ejpam-2985	296	5	that	that	SCONJ
ejpam-2985	296	6	gu	gu	NOUN
ejpam-2985	296	7	=	=	SYM
ejpam-2985	296	8	su	su	PROPN
ejpam-2985	296	9	.	.	PROPN
ejpam-2985	296	10	given	give	VERB
ejpam-2985	296	11	c	c	PROPN
ejpam-2985	296	12	�	�	PROPN
ejpam-2985	296	13	0	0	NUM
ejpam-2985	296	14	,	,	PUNCT
ejpam-2985	296	15	we	we	PRON
ejpam-2985	296	16	choose	choose	VERB
ejpam-2985	296	17	a	a	DET
ejpam-2985	296	18	natural	natural	ADJ
ejpam-2985	296	19	numbers	number	NOUN
ejpam-2985	296	20	m1,m2,m3	m1,m2,m3	ADJ
ejpam-2985	296	21	such	such	ADJ
ejpam-2985	296	22	that	that	SCONJ
ejpam-2985	296	23	d(v	d(v	PROPN
ejpam-2985	296	24	,	,	PUNCT
ejpam-2985	296	25	gxn	gxn	ADJ
ejpam-2985	296	26	)	)	PUNCT
ejpam-2985	296	27	�	�	PROPN
ejpam-2985	296	28	c(1−λ	c(1−λ	PROPN
ejpam-2985	296	29	)	)	PUNCT
ejpam-2985	296	30	3	3	NUM
ejpam-2985	296	31	,	,	PUNCT
ejpam-2985	296	32	∀n	∀n	NUM
ejpam-2985	296	33	≥	≥	NOUN
ejpam-2985	296	34	m1	m1	NOUN
ejpam-2985	296	35	,	,	PUNCT
ejpam-2985	296	36	d(gxn	d(gxn	PROPN
ejpam-2985	296	37	,	,	PUNCT
ejpam-2985	296	38	gxn+1	gxn+1	PROPN
ejpam-2985	296	39	)	)	PUNCT
ejpam-2985	296	40	�	�	PROPN
ejpam-2985	296	41	c(1−λ	c(1−λ	PROPN
ejpam-2985	296	42	)	)	PUNCT
ejpam-2985	296	43	3	3	NUM
ejpam-2985	296	44	,	,	PUNCT
ejpam-2985	296	45	∀n	∀n	NUM
ejpam-2985	296	46	≥	≥	NOUN
ejpam-2985	296	47	m2	m2	PROPN
ejpam-2985	296	48	and	and	CCONJ
ejpam-2985	296	49	d(gxn+1	d(gxn+1	PROPN
ejpam-2985	296	50	,	,	PUNCT
ejpam-2985	296	51	gxn+2	gxn+2	PROPN
ejpam-2985	296	52	)	)	PUNCT
ejpam-2985	296	53	�	�	PROPN
ejpam-2985	296	54	c(1−λ	c(1−λ	PROPN
ejpam-2985	296	55	)	)	PUNCT
ejpam-2985	296	56	3(1+λ	3(1+λ	NUM
ejpam-2985	296	57	)	)	PUNCT
ejpam-2985	296	58	,	,	PUNCT
ejpam-2985	297	1	∀n	∀n	NUM
ejpam-2985	297	2	≥m3	≥m3	NOUN
ejpam-2985	297	3	.	.	PUNCT
ejpam-2985	298	1	since	since	SCONJ
ejpam-2985	298	2	xn	xn	PROPN
ejpam-2985	298	3	6=	6=	NUM
ejpam-2985	298	4	xm	xm	PROPN
ejpam-2985	298	5	for	for	ADP
ejpam-2985	298	6	n	n	PROPN
ejpam-2985	298	7	6=	6=	NUM
ejpam-2985	298	8	m	m	PROPN
ejpam-2985	298	9	,	,	PUNCT
ejpam-2985	298	10	by	by	ADP
ejpam-2985	298	11	pentagonal	pentagonal	ADJ
ejpam-2985	298	12	property	property	NOUN
ejpam-2985	298	13	,	,	PUNCT
ejpam-2985	298	14	we	we	PRON
ejpam-2985	298	15	have	have	VERB
ejpam-2985	298	16	that	that	DET
ejpam-2985	298	17	d(gu	d(gu	PROPN
ejpam-2985	298	18	,	,	PUNCT
ejpam-2985	298	19	su	su	NOUN
ejpam-2985	298	20	)	)	PUNCT
ejpam-2985	298	21	≤	≤	NOUN
ejpam-2985	298	22	d(gu	d(gu	PROPN
ejpam-2985	298	23	,	,	PUNCT
ejpam-2985	298	24	gxn	gxn	PROPN
ejpam-2985	298	25	)	)	PUNCT
ejpam-2985	298	26	+	+	CCONJ
ejpam-2985	298	27	d(gxn	d(gxn	PROPN
ejpam-2985	298	28	,	,	PUNCT
ejpam-2985	298	29	gxn+1	gxn+1	NOUN
ejpam-2985	298	30	)	)	PUNCT
ejpam-2985	299	1	+	+	CCONJ
ejpam-2985	299	2	d(gxn+1	d(gxn+1	NOUN
ejpam-2985	299	3	,	,	PUNCT
ejpam-2985	299	4	gxn+2	gxn+2	PROPN
ejpam-2985	299	5	)	)	PUNCT
ejpam-2985	300	1	+	+	CCONJ
ejpam-2985	300	2	d(gxn+2	d(gxn+2	PROPN
ejpam-2985	300	3	,	,	PUNCT
ejpam-2985	300	4	su	su	NOUN
ejpam-2985	300	5	)	)	PUNCT
ejpam-2985	300	6	a.	a.	NOUN
ejpam-2985	300	7	auwalu	auwalu	PROPN
ejpam-2985	300	8	,	,	PUNCT
ejpam-2985	300	9	e.	e.	PROPN
ejpam-2985	300	10	hınçal	hınçal	PROPN
ejpam-2985	300	11	/	/	SYM
ejpam-2985	300	12	eur	eur	PROPN
ejpam-2985	300	13	.	.	PUNCT
ejpam-2985	301	1	j.	j.	PROPN
ejpam-2985	301	2	pure	pure	PROPN
ejpam-2985	301	3	appl	appl	PROPN
ejpam-2985	301	4	.	.	PROPN
ejpam-2985	301	5	math	math	PROPN
ejpam-2985	301	6	,	,	PUNCT
ejpam-2985	301	7	10	10	NUM
ejpam-2985	301	8	(	(	PUNCT
ejpam-2985	301	9	3	3	NUM
ejpam-2985	301	10	)	)	PUNCT
ejpam-2985	301	11	(	(	PUNCT
ejpam-2985	301	12	2017	2017	NUM
ejpam-2985	301	13	)	)	PUNCT
ejpam-2985	301	14	,	,	PUNCT
ejpam-2985	301	15	473	473	NUM
ejpam-2985	301	16	-	-	SYM
ejpam-2985	301	17	487	487	NUM
ejpam-2985	301	18	484	484	NUM
ejpam-2985	301	19	≤	≤	NOUN
ejpam-2985	301	20	d(v	d(v	PROPN
ejpam-2985	301	21	,	,	PUNCT
ejpam-2985	301	22	gxn	gxn	ADJ
ejpam-2985	301	23	)	)	PUNCT
ejpam-2985	301	24	+	+	CCONJ
ejpam-2985	301	25	d(gxn	d(gxn	PROPN
ejpam-2985	301	26	,	,	PUNCT
ejpam-2985	301	27	gxn+1	gxn+1	NOUN
ejpam-2985	301	28	)	)	PUNCT
ejpam-2985	301	29	+	+	CCONJ
ejpam-2985	301	30	d(gxn+1	d(gxn+1	NOUN
ejpam-2985	301	31	,	,	PUNCT
ejpam-2985	301	32	gxn+2	gxn+2	PROPN
ejpam-2985	301	33	)	)	PUNCT
ejpam-2985	302	1	+	+	CCONJ
ejpam-2985	302	2	d(fxn+1	d(fxn+1	PROPN
ejpam-2985	302	3	,	,	PUNCT
ejpam-2985	302	4	su	su	NOUN
ejpam-2985	302	5	)	)	PUNCT
ejpam-2985	302	6	≤	≤	NOUN
ejpam-2985	303	1	d(v	d(v	PROPN
ejpam-2985	303	2	,	,	PUNCT
ejpam-2985	303	3	gxn	gxn	ADJ
ejpam-2985	303	4	)	)	PUNCT
ejpam-2985	303	5	+	+	CCONJ
ejpam-2985	303	6	d(gxn	d(gxn	PROPN
ejpam-2985	303	7	,	,	PUNCT
ejpam-2985	303	8	gxn+1	gxn+1	NOUN
ejpam-2985	303	9	)	)	PUNCT
ejpam-2985	303	10	+	+	CCONJ
ejpam-2985	303	11	d(gxn+1	d(gxn+1	NOUN
ejpam-2985	303	12	,	,	PUNCT
ejpam-2985	303	13	gxn+2	gxn+2	PROPN
ejpam-2985	303	14	)	)	PUNCT
ejpam-2985	304	1	+	+	CCONJ
ejpam-2985	304	2	λ	λ	X
ejpam-2985	304	3	(	(	PUNCT
ejpam-2985	304	4	d(gu	d(gu	PROPN
ejpam-2985	304	5	,	,	PUNCT
ejpam-2985	304	6	su	su	NOUN
ejpam-2985	304	7	)	)	PUNCT
ejpam-2985	304	8	+	+	CCONJ
ejpam-2985	304	9	d(gxn+1	d(gxn+1	NOUN
ejpam-2985	304	10	,	,	PUNCT
ejpam-2985	304	11	fxn+1	fxn+1	PROPN
ejpam-2985	304	12	)	)	PUNCT
ejpam-2985	304	13	)	)	PUNCT
ejpam-2985	305	1	<	<	X
ejpam-2985	305	2	d(v	d(v	PROPN
ejpam-2985	305	3	,	,	PUNCT
ejpam-2985	305	4	gxn	gxn	ADJ
ejpam-2985	305	5	)	)	PUNCT
ejpam-2985	305	6	+	+	CCONJ
ejpam-2985	305	7	d(gxn	d(gxn	PROPN
ejpam-2985	305	8	,	,	PUNCT
ejpam-2985	305	9	gxn+1	gxn+1	NOUN
ejpam-2985	305	10	)	)	PUNCT
ejpam-2985	305	11	+	+	CCONJ
ejpam-2985	305	12	d(gxn+1	d(gxn+1	NOUN
ejpam-2985	305	13	,	,	PUNCT
ejpam-2985	305	14	gxn+2	gxn+2	PROPN
ejpam-2985	305	15	)	)	PUNCT
ejpam-2985	306	1	+	+	CCONJ
ejpam-2985	306	2	λ	λ	X
ejpam-2985	306	3	(	(	PUNCT
ejpam-2985	306	4	d(gu	d(gu	PROPN
ejpam-2985	306	5	,	,	PUNCT
ejpam-2985	306	6	su	su	NOUN
ejpam-2985	306	7	)	)	PUNCT
ejpam-2985	306	8	+	+	CCONJ
ejpam-2985	306	9	d(gxn+1	d(gxn+1	NOUN
ejpam-2985	306	10	,	,	PUNCT
ejpam-2985	306	11	gxn+2	gxn+2	PROPN
ejpam-2985	306	12	)	)	PUNCT
ejpam-2985	306	13	)	)	PUNCT
ejpam-2985	306	14	d(gu	d(gu	PROPN
ejpam-2985	306	15	,	,	PUNCT
ejpam-2985	306	16	su	su	NOUN
ejpam-2985	306	17	)	)	PUNCT
ejpam-2985	306	18	≤	≤	NOUN
ejpam-2985	306	19	1	1	NUM
ejpam-2985	306	20	1−	1−	NUM
ejpam-2985	306	21	λ	λ	X
ejpam-2985	306	22	(	(	PUNCT
ejpam-2985	306	23	d(v	d(v	PROPN
ejpam-2985	306	24	,	,	PUNCT
ejpam-2985	306	25	gxn	gxn	ADJ
ejpam-2985	306	26	)	)	PUNCT
ejpam-2985	306	27	+	+	CCONJ
ejpam-2985	306	28	d(gxn	d(gxn	PROPN
ejpam-2985	306	29	,	,	PUNCT
ejpam-2985	306	30	gxn+1	gxn+1	PROPN
ejpam-2985	306	31	)	)	PUNCT
ejpam-2985	307	1	+	+	CCONJ
ejpam-2985	307	2	(	(	PUNCT
ejpam-2985	307	3	1	1	NUM
ejpam-2985	307	4	+	+	CCONJ
ejpam-2985	307	5	λ)d(gxn+1	λ)d(gxn+1	ADJ
ejpam-2985	307	6	,	,	PUNCT
ejpam-2985	307	7	gxn+2	gxn+2	PROPN
ejpam-2985	307	8	)	)	PUNCT
ejpam-2985	307	9	)	)	PUNCT
ejpam-2985	308	1	�	�	PROPN
ejpam-2985	308	2	c	c	NOUN
ejpam-2985	308	3	3	3	NUM
ejpam-2985	308	4	+	+	CCONJ
ejpam-2985	308	5	c	c	NOUN
ejpam-2985	308	6	3	3	NUM
ejpam-2985	308	7	+	+	CCONJ
ejpam-2985	308	8	c	c	NOUN
ejpam-2985	308	9	3	3	NUM
ejpam-2985	308	10	=	=	SYM
ejpam-2985	308	11	c	c	NOUN
ejpam-2985	308	12	,	,	PUNCT
ejpam-2985	308	13	for	for	ADP
ejpam-2985	308	14	all	all	DET
ejpam-2985	308	15	n	n	DET
ejpam-2985	308	16	≥m	≥m	NOUN
ejpam-2985	308	17	,	,	PUNCT
ejpam-2985	308	18	where	where	SCONJ
ejpam-2985	308	19	m	m	VERB
ejpam-2985	308	20	:	:	PUNCT
ejpam-2985	308	21	=	=	PUNCT
ejpam-2985	308	22	max{m1,m2,m3	max{m1,m2,m3	NOUN
ejpam-2985	308	23	}	}	PUNCT
ejpam-2985	308	24	.	.	PUNCT
ejpam-2985	309	1	since	since	SCONJ
ejpam-2985	309	2	c	c	PROPN
ejpam-2985	309	3	is	be	AUX
ejpam-2985	309	4	arbitrary	arbitrary	ADJ
ejpam-2985	309	5	,	,	PUNCT
ejpam-2985	309	6	we	we	PRON
ejpam-2985	309	7	have	have	VERB
ejpam-2985	309	8	d(gu	d(gu	PROPN
ejpam-2985	309	9	,	,	PUNCT
ejpam-2985	309	10	su	su	PROPN
ejpam-2985	309	11	)	)	PUNCT
ejpam-2985	309	12	�	�	PROPN
ejpam-2985	309	13	c	c	NOUN
ejpam-2985	309	14	m	m	PROPN
ejpam-2985	309	15	,	,	PUNCT
ejpam-2985	309	16	∀m	∀m	PROPN
ejpam-2985	309	17	∈	∈	PROPN
ejpam-2985	309	18	n.	n.	NOUN
ejpam-2985	309	19	since	since	SCONJ
ejpam-2985	309	20	c	c	PROPN
ejpam-2985	309	21	m	m	PROPN
ejpam-2985	309	22	→	→	SYM
ejpam-2985	309	23	0	0	NUM
ejpam-2985	310	1	as	as	SCONJ
ejpam-2985	310	2	m	m	PROPN
ejpam-2985	310	3	→	→	SYM
ejpam-2985	310	4	∞	∞	PROPN
ejpam-2985	310	5	,	,	PUNCT
ejpam-2985	310	6	we	we	PRON
ejpam-2985	310	7	conclude	conclude	VERB
ejpam-2985	310	8	c	c	PROPN
ejpam-2985	310	9	m	m	VERB
ejpam-2985	310	10	−	−	PROPN
ejpam-2985	310	11	d(gu	d(gu	PROPN
ejpam-2985	310	12	,	,	PUNCT
ejpam-2985	310	13	su	su	NOUN
ejpam-2985	310	14	)	)	PUNCT
ejpam-2985	310	15	→	→	SYM
ejpam-2985	310	16	−d(gu	−d(gu	PROPN
ejpam-2985	310	17	,	,	PUNCT
ejpam-2985	310	18	su	su	PROPN
ejpam-2985	310	19	)	)	PUNCT
ejpam-2985	310	20	as	as	ADP
ejpam-2985	310	21	m	m	PROPN
ejpam-2985	310	22	→	→	SYM
ejpam-2985	310	23	∞.	∞.	PROPN
ejpam-2985	310	24	since	since	SCONJ
ejpam-2985	310	25	p	p	NOUN
ejpam-2985	310	26	is	be	AUX
ejpam-2985	310	27	closed	closed	ADJ
ejpam-2985	310	28	,	,	PUNCT
ejpam-2985	311	1	−d(gu	−d(gu	NOUN
ejpam-2985	311	2	,	,	PUNCT
ejpam-2985	311	3	su	su	PROPN
ejpam-2985	311	4	)	)	PUNCT
ejpam-2985	311	5	∈	∈	PROPN
ejpam-2985	311	6	p.	p.	NOUN
ejpam-2985	311	7	hence	hence	ADV
ejpam-2985	311	8	d(gu	d(gu	PROPN
ejpam-2985	311	9	,	,	PUNCT
ejpam-2985	311	10	su	su	NOUN
ejpam-2985	311	11	)	)	PUNCT
ejpam-2985	311	12	∈	∈	PROPN
ejpam-2985	311	13	p	p	NOUN
ejpam-2985	311	14	∩	∩	ADJ
ejpam-2985	311	15	−p	−p	NOUN
ejpam-2985	311	16	.	.	PUNCT
ejpam-2985	312	1	by	by	ADP
ejpam-2985	312	2	definition	definition	NOUN
ejpam-2985	312	3	of	of	ADP
ejpam-2985	312	4	cone	cone	NOUN
ejpam-2985	312	5	we	we	PRON
ejpam-2985	312	6	get	get	VERB
ejpam-2985	312	7	that	that	DET
ejpam-2985	312	8	d(gu	d(gu	PROPN
ejpam-2985	312	9	,	,	PUNCT
ejpam-2985	312	10	su	su	NOUN
ejpam-2985	312	11	)	)	PUNCT
ejpam-2985	312	12	=	=	SYM
ejpam-2985	312	13	0	0	NUM
ejpam-2985	312	14	,	,	PUNCT
ejpam-2985	312	15	and	and	CCONJ
ejpam-2985	312	16	so	so	ADV
ejpam-2985	312	17	gu	gu	NOUN
ejpam-2985	312	18	=	=	SYM
ejpam-2985	312	19	su	su	PROPN
ejpam-2985	313	1	=	=	NOUN
ejpam-2985	313	2	v.	v.	ADP
ejpam-2985	313	3	hence	hence	ADV
ejpam-2985	313	4	,	,	PUNCT
ejpam-2985	313	5	v	v	PRON
ejpam-2985	313	6	is	be	AUX
ejpam-2985	313	7	a	a	DET
ejpam-2985	313	8	point	point	NOUN
ejpam-2985	313	9	of	of	ADP
ejpam-2985	313	10	coincidence	coincidence	NOUN
ejpam-2985	313	11	of	of	ADP
ejpam-2985	313	12	s	s	PRON
ejpam-2985	313	13	and	and	CCONJ
ejpam-2985	313	14	g.	g.	PROPN
ejpam-2985	313	15	similarly	similarly	ADV
ejpam-2985	313	16	,	,	PUNCT
ejpam-2985	313	17	we	we	PRON
ejpam-2985	313	18	can	can	AUX
ejpam-2985	313	19	prove	prove	VERB
ejpam-2985	313	20	that	that	DET
ejpam-2985	313	21	gu	gu	NOUN
ejpam-2985	313	22	=	=	PUNCT
ejpam-2985	313	23	fu	fu	NOUN
ejpam-2985	313	24	=	=	SYM
ejpam-2985	313	25	v	v	NOUN
ejpam-2985	313	26	,	,	PUNCT
ejpam-2985	313	27	which	which	PRON
ejpam-2985	313	28	implies	imply	VERB
ejpam-2985	313	29	that	that	SCONJ
ejpam-2985	313	30	v	v	NOUN
ejpam-2985	313	31	is	be	AUX
ejpam-2985	313	32	a	a	DET
ejpam-2985	313	33	point	point	NOUN
ejpam-2985	313	34	of	of	ADP
ejpam-2985	313	35	coincidence	coincidence	NOUN
ejpam-2985	313	36	of	of	ADP
ejpam-2985	313	37	s	s	PROPN
ejpam-2985	313	38	,	,	PUNCT
ejpam-2985	313	39	f	f	PROPN
ejpam-2985	313	40	and	and	CCONJ
ejpam-2985	313	41	g	g	PROPN
ejpam-2985	313	42	,	,	PUNCT
ejpam-2985	313	43	i.e.	i.e.	X
ejpam-2985	313	44	gu	gu	X
ejpam-2985	313	45	=	=	PUNCT
ejpam-2985	313	46	fu	fu	NOUN
ejpam-2985	313	47	=	=	PUNCT
ejpam-2985	313	48	su	su	PROPN
ejpam-2985	314	1	=	=	PROPN
ejpam-2985	314	2	v.	v.	ADP
ejpam-2985	314	3	next	next	ADV
ejpam-2985	314	4	,	,	PUNCT
ejpam-2985	314	5	we	we	PRON
ejpam-2985	314	6	show	show	VERB
ejpam-2985	314	7	that	that	SCONJ
ejpam-2985	314	8	v	v	NOUN
ejpam-2985	314	9	is	be	AUX
ejpam-2985	314	10	unique	unique	ADJ
ejpam-2985	314	11	.	.	PUNCT
ejpam-2985	315	1	for	for	ADP
ejpam-2985	315	2	suppose	suppose	VERB
ejpam-2985	315	3	v′	v′	NOUN
ejpam-2985	315	4	be	be	AUX
ejpam-2985	315	5	another	another	DET
ejpam-2985	315	6	point	point	NOUN
ejpam-2985	315	7	of	of	ADP
ejpam-2985	315	8	coincidence	coincidence	NOUN
ejpam-2985	315	9	,	,	PUNCT
ejpam-2985	315	10	that	that	ADV
ejpam-2985	315	11	is	be	AUX
ejpam-2985	315	12	gu′	gu′	NOUN
ejpam-2985	315	13	=	=	SYM
ejpam-2985	315	14	fu′	fu′	NOUN
ejpam-2985	315	15	=	=	SYM
ejpam-2985	315	16	su′	su′	NOUN
ejpam-2985	315	17	=	=	SYM
ejpam-2985	315	18	v′	v′	NOUN
ejpam-2985	315	19	,	,	PUNCT
ejpam-2985	315	20	for	for	ADP
ejpam-2985	315	21	some	some	DET
ejpam-2985	315	22	u′	u′	PROPN
ejpam-2985	315	23	∈	∈	PROPN
ejpam-2985	315	24	x	x	NOUN
ejpam-2985	315	25	,	,	PUNCT
ejpam-2985	315	26	then	then	ADV
ejpam-2985	315	27	d(v	d(v	PROPN
ejpam-2985	315	28	,	,	PUNCT
ejpam-2985	315	29	v′	v′	NOUN
ejpam-2985	315	30	)	)	PUNCT
ejpam-2985	316	1	=	=	PUNCT
ejpam-2985	316	2	d(su	d(su	ADJ
ejpam-2985	316	3	,	,	PUNCT
ejpam-2985	316	4	fu′	fu′	NOUN
ejpam-2985	316	5	)	)	PUNCT
ejpam-2985	316	6	≤	≤	NUM
ejpam-2985	316	7	λ	λ	PROPN
ejpam-2985	316	8	(	(	PUNCT
ejpam-2985	316	9	d(gu	d(gu	PROPN
ejpam-2985	316	10	,	,	PUNCT
ejpam-2985	316	11	su	su	NOUN
ejpam-2985	316	12	)	)	PUNCT
ejpam-2985	316	13	+	+	CCONJ
ejpam-2985	316	14	d(gu′	d(gu′	PROPN
ejpam-2985	316	15	,	,	PUNCT
ejpam-2985	316	16	fu′	fu′	NOUN
ejpam-2985	316	17	)	)	PUNCT
ejpam-2985	316	18	)	)	PUNCT
ejpam-2985	317	1	≤	≤	NUM
ejpam-2985	317	2	λ	λ	PROPN
ejpam-2985	317	3	(	(	PUNCT
ejpam-2985	317	4	d(v	d(v	PROPN
ejpam-2985	317	5	,	,	PUNCT
ejpam-2985	317	6	v	v	NOUN
ejpam-2985	317	7	)	)	PUNCT
ejpam-2985	317	8	+	+	CCONJ
ejpam-2985	317	9	d(v′	d(v′	PROPN
ejpam-2985	317	10	,	,	PUNCT
ejpam-2985	317	11	v′	v′	PROPN
ejpam-2985	317	12	)	)	PUNCT
ejpam-2985	317	13	)	)	PUNCT
ejpam-2985	317	14	.	.	PUNCT
ejpam-2985	318	1	hence	hence	ADV
ejpam-2985	318	2	v	v	NOUN
ejpam-2985	318	3	=	=	X
ejpam-2985	318	4	v′.	v′.	INTJ
ejpam-2985	318	5	since	since	SCONJ
ejpam-2985	318	6	(	(	PUNCT
ejpam-2985	318	7	s	s	X
ejpam-2985	318	8	,	,	PUNCT
ejpam-2985	318	9	g	g	NOUN
ejpam-2985	318	10	)	)	PUNCT
ejpam-2985	318	11	and	and	CCONJ
ejpam-2985	318	12	(	(	PUNCT
ejpam-2985	318	13	f	f	X
ejpam-2985	318	14	,	,	PUNCT
ejpam-2985	318	15	g	g	NOUN
ejpam-2985	318	16	)	)	PUNCT
ejpam-2985	318	17	are	be	AUX
ejpam-2985	318	18	weakly	weakly	ADV
ejpam-2985	318	19	compatible	compatible	ADJ
ejpam-2985	318	20	,	,	PUNCT
ejpam-2985	318	21	by	by	ADP
ejpam-2985	318	22	lemma	lemma	PROPN
ejpam-2985	318	23	1	1	NUM
ejpam-2985	318	24	,	,	PUNCT
ejpam-2985	318	25	v	v	NOUN
ejpam-2985	318	26	is	be	AUX
ejpam-2985	318	27	the	the	DET
ejpam-2985	318	28	unique	unique	ADJ
ejpam-2985	318	29	common	common	ADJ
ejpam-2985	318	30	fixed	fix	VERB
ejpam-2985	318	31	point	point	NOUN
ejpam-2985	318	32	of	of	ADP
ejpam-2985	318	33	s	s	PROPN
ejpam-2985	318	34	,	,	PUNCT
ejpam-2985	318	35	f	f	PROPN
ejpam-2985	318	36	and	and	CCONJ
ejpam-2985	318	37	g.	g.	PROPN
ejpam-2985	318	38	this	this	PRON
ejpam-2985	318	39	completes	complete	VERB
ejpam-2985	318	40	the	the	DET
ejpam-2985	318	41	proof	proof	NOUN
ejpam-2985	318	42	of	of	ADP
ejpam-2985	318	43	the	the	DET
ejpam-2985	318	44	theorem	theorem	PROPN
ejpam-2985	318	45	.	.	PROPN
ejpam-2985	318	46	corollary	corollary	ADJ
ejpam-2985	318	47	10	10	NUM
ejpam-2985	318	48	.	.	PUNCT
ejpam-2985	319	1	(	(	PUNCT
ejpam-2985	319	2	see	see	VERB
ejpam-2985	319	3	[	[	X
ejpam-2985	319	4	5	5	NUM
ejpam-2985	319	5	]	]	PUNCT
ejpam-2985	319	6	)	)	PUNCT
ejpam-2985	319	7	let	let	VERB
ejpam-2985	319	8	(	(	PUNCT
ejpam-2985	319	9	x	x	NOUN
ejpam-2985	319	10	,	,	PUNCT
ejpam-2985	319	11	d	d	NOUN
ejpam-2985	319	12	)	)	PUNCT
ejpam-2985	319	13	be	be	AUX
ejpam-2985	319	14	a	a	DET
ejpam-2985	319	15	cone	cone	NOUN
ejpam-2985	319	16	pentagonal	pentagonal	ADJ
ejpam-2985	319	17	metric	metric	ADJ
ejpam-2985	319	18	space	space	NOUN
ejpam-2985	319	19	.	.	PUNCT
ejpam-2985	320	1	suppose	suppose	VERB
ejpam-2985	320	2	the	the	DET
ejpam-2985	320	3	mappings	mapping	NOUN
ejpam-2985	320	4	s	s	PART
ejpam-2985	320	5	,	,	PUNCT
ejpam-2985	320	6	g	g	NOUN
ejpam-2985	320	7	:	:	PUNCT
ejpam-2985	320	8	x	x	SYM
ejpam-2985	320	9	→	→	PUNCT
ejpam-2985	320	10	x	x	SYM
ejpam-2985	320	11	satisfies	satisfy	VERB
ejpam-2985	320	12	the	the	DET
ejpam-2985	320	13	contractive	contractive	ADJ
ejpam-2985	320	14	condition	condition	NOUN
ejpam-2985	320	15	:	:	PUNCT
ejpam-2985	320	16	d(sx	d(sx	NOUN
ejpam-2985	320	17	,	,	PUNCT
ejpam-2985	320	18	sy	sy	NOUN
ejpam-2985	320	19	)	)	PUNCT
ejpam-2985	320	20	≤	≤	NUM
ejpam-2985	321	1	λ	λ	PROPN
ejpam-2985	321	2	[	[	PUNCT
ejpam-2985	321	3	d(gx	d(gx	PROPN
ejpam-2985	321	4	,	,	PUNCT
ejpam-2985	321	5	sx	sx	PROPN
ejpam-2985	321	6	)	)	PUNCT
ejpam-2985	321	7	+	+	NUM
ejpam-2985	321	8	d(gy	d(gy	PROPN
ejpam-2985	321	9	,	,	PUNCT
ejpam-2985	321	10	sy	sy	PROPN
ejpam-2985	321	11	)	)	PUNCT
ejpam-2985	321	12	]	]	PUNCT
ejpam-2985	321	13	,	,	PUNCT
ejpam-2985	321	14	for	for	ADP
ejpam-2985	321	15	all	all	DET
ejpam-2985	321	16	x	x	NOUN
ejpam-2985	321	17	,	,	PUNCT
ejpam-2985	321	18	y	y	PROPN
ejpam-2985	321	19	∈	∈	PROPN
ejpam-2985	321	20	x	x	NOUN
ejpam-2985	321	21	,	,	PUNCT
ejpam-2985	321	22	where	where	SCONJ
ejpam-2985	321	23	λ	λ	PROPN
ejpam-2985	321	24	∈	∈	PROPN
ejpam-2985	322	1	[	[	X
ejpam-2985	322	2	0	0	NUM
ejpam-2985	322	3	,	,	PUNCT
ejpam-2985	322	4	1/2	1/2	NUM
ejpam-2985	322	5	)	)	PUNCT
ejpam-2985	322	6	.	.	PUNCT
ejpam-2985	323	1	suppose	suppose	VERB
ejpam-2985	323	2	that	that	SCONJ
ejpam-2985	323	3	s(x	s(x	NOUN
ejpam-2985	323	4	)	)	PUNCT
ejpam-2985	323	5	⊆	⊆	NUM
ejpam-2985	323	6	g(x	g(x	NOUN
ejpam-2985	323	7	)	)	PUNCT
ejpam-2985	323	8	,	,	PUNCT
ejpam-2985	323	9	and	and	CCONJ
ejpam-2985	323	10	s(x	s(x	NOUN
ejpam-2985	323	11	)	)	PUNCT
ejpam-2985	323	12	or	or	CCONJ
ejpam-2985	323	13	g(x	g(x	NOUN
ejpam-2985	323	14	)	)	PUNCT
ejpam-2985	323	15	is	be	AUX
ejpam-2985	323	16	a	a	DET
ejpam-2985	323	17	complete	complete	ADJ
ejpam-2985	323	18	subspace	subspace	NOUN
ejpam-2985	323	19	of	of	ADP
ejpam-2985	323	20	x	x	PRON
ejpam-2985	323	21	,	,	PUNCT
ejpam-2985	323	22	then	then	ADV
ejpam-2985	323	23	the	the	DET
ejpam-2985	323	24	mappings	mapping	NOUN
ejpam-2985	323	25	s	s	PART
ejpam-2985	323	26	and	and	CCONJ
ejpam-2985	323	27	g	g	PROPN
ejpam-2985	323	28	have	have	VERB
ejpam-2985	323	29	a	a	DET
ejpam-2985	323	30	unique	unique	ADJ
ejpam-2985	323	31	point	point	NOUN
ejpam-2985	323	32	of	of	ADP
ejpam-2985	323	33	coincidence	coincidence	NOUN
ejpam-2985	323	34	in	in	ADP
ejpam-2985	323	35	x.	x.	NOUN
ejpam-2985	323	36	moreover	moreover	ADV
ejpam-2985	323	37	,	,	PUNCT
ejpam-2985	323	38	if	if	SCONJ
ejpam-2985	323	39	s	s	X
ejpam-2985	323	40	and	and	CCONJ
ejpam-2985	323	41	g	g	PROPN
ejpam-2985	323	42	are	be	AUX
ejpam-2985	323	43	weakly	weakly	ADV
ejpam-2985	323	44	compatible	compatible	ADJ
ejpam-2985	323	45	then	then	ADV
ejpam-2985	323	46	s	s	VERB
ejpam-2985	323	47	and	and	CCONJ
ejpam-2985	323	48	g	g	PROPN
ejpam-2985	323	49	have	have	VERB
ejpam-2985	323	50	a	a	DET
ejpam-2985	323	51	unique	unique	ADJ
ejpam-2985	323	52	common	common	ADJ
ejpam-2985	323	53	fixed	fix	VERB
ejpam-2985	323	54	point	point	NOUN
ejpam-2985	323	55	in	in	ADP
ejpam-2985	323	56	x.	x.	NOUN
ejpam-2985	323	57	proof	proof	NOUN
ejpam-2985	323	58	.	.	PUNCT
ejpam-2985	324	1	putting	put	VERB
ejpam-2985	324	2	f	f	NOUN
ejpam-2985	324	3	=	=	SYM
ejpam-2985	324	4	s	s	PROPN
ejpam-2985	324	5	in	in	ADP
ejpam-2985	324	6	theorem	theorem	NOUN
ejpam-2985	324	7	2	2	NUM
ejpam-2985	324	8	.	.	PUNCT
ejpam-2985	325	1	this	this	PRON
ejpam-2985	325	2	completes	complete	VERB
ejpam-2985	325	3	the	the	DET
ejpam-2985	325	4	proof	proof	NOUN
ejpam-2985	325	5	.	.	PUNCT
ejpam-2985	326	1	corollary	corollary	ADJ
ejpam-2985	326	2	11	11	NUM
ejpam-2985	326	3	.	.	PUNCT
ejpam-2985	327	1	(	(	PUNCT
ejpam-2985	327	2	see	see	VERB
ejpam-2985	327	3	[	[	X
ejpam-2985	327	4	16	16	NUM
ejpam-2985	327	5	]	]	PUNCT
ejpam-2985	327	6	)	)	PUNCT
ejpam-2985	327	7	let	let	VERB
ejpam-2985	327	8	(	(	PUNCT
ejpam-2985	327	9	x	x	NOUN
ejpam-2985	327	10	,	,	PUNCT
ejpam-2985	327	11	d	d	NOUN
ejpam-2985	327	12	)	)	PUNCT
ejpam-2985	327	13	be	be	AUX
ejpam-2985	327	14	a	a	DET
ejpam-2985	327	15	cone	cone	NOUN
ejpam-2985	327	16	rectangular	rectangular	ADJ
ejpam-2985	327	17	metric	metric	ADJ
ejpam-2985	327	18	space	space	NOUN
ejpam-2985	327	19	.	.	PUNCT
ejpam-2985	328	1	suppose	suppose	VERB
ejpam-2985	328	2	the	the	DET
ejpam-2985	328	3	mappings	mapping	NOUN
ejpam-2985	328	4	s	s	PART
ejpam-2985	328	5	,	,	PUNCT
ejpam-2985	328	6	f	f	PROPN
ejpam-2985	328	7	,	,	PUNCT
ejpam-2985	328	8	g	g	NOUN
ejpam-2985	328	9	:	:	PUNCT
ejpam-2985	328	10	x	x	SYM
ejpam-2985	328	11	→	→	PUNCT
ejpam-2985	328	12	x	x	SYM
ejpam-2985	328	13	satisfies	satisfy	VERB
ejpam-2985	328	14	the	the	DET
ejpam-2985	328	15	contractive	contractive	ADJ
ejpam-2985	328	16	condition	condition	NOUN
ejpam-2985	328	17	:	:	PUNCT
ejpam-2985	328	18	d(sx	d(sx	PROPN
ejpam-2985	328	19	,	,	PUNCT
ejpam-2985	328	20	fy	fy	NOUN
ejpam-2985	328	21	)	)	PUNCT
ejpam-2985	328	22	≤	≤	NOUN
ejpam-2985	329	1	λ	λ	PROPN
ejpam-2985	329	2	[	[	PUNCT
ejpam-2985	329	3	d(gx	d(gx	PROPN
ejpam-2985	329	4	,	,	PUNCT
ejpam-2985	329	5	sx	sx	PROPN
ejpam-2985	329	6	)	)	PUNCT
ejpam-2985	329	7	+	+	NUM
ejpam-2985	329	8	d(gy	d(gy	PROPN
ejpam-2985	329	9	,	,	PUNCT
ejpam-2985	329	10	fy	fy	PROPN
ejpam-2985	329	11	)	)	PUNCT
ejpam-2985	329	12	]	]	PUNCT
ejpam-2985	329	13	,	,	PUNCT
ejpam-2985	329	14	for	for	ADP
ejpam-2985	329	15	all	all	DET
ejpam-2985	329	16	x	x	NOUN
ejpam-2985	329	17	,	,	PUNCT
ejpam-2985	329	18	y	y	PROPN
ejpam-2985	329	19	∈	∈	PROPN
ejpam-2985	329	20	x	x	NOUN
ejpam-2985	329	21	,	,	PUNCT
ejpam-2985	329	22	where	where	SCONJ
ejpam-2985	329	23	λ	λ	PROPN
ejpam-2985	329	24	∈	∈	PROPN
ejpam-2985	330	1	[	[	X
ejpam-2985	330	2	0	0	NUM
ejpam-2985	330	3	,	,	PUNCT
ejpam-2985	330	4	1/2	1/2	NUM
ejpam-2985	330	5	)	)	PUNCT
ejpam-2985	330	6	.	.	PUNCT
ejpam-2985	331	1	suppose	suppose	VERB
ejpam-2985	331	2	that	that	SCONJ
ejpam-2985	331	3	s(x	s(x	NOUN
ejpam-2985	331	4	)	)	PUNCT
ejpam-2985	331	5	∪	∪	ADP
ejpam-2985	331	6	f(x	f(x	PROPN
ejpam-2985	331	7	)	)	PUNCT
ejpam-2985	331	8	⊆	⊆	NUM
ejpam-2985	331	9	g(x	g(x	NOUN
ejpam-2985	331	10	)	)	PUNCT
ejpam-2985	331	11	,	,	PUNCT
ejpam-2985	331	12	and	and	CCONJ
ejpam-2985	331	13	g(x	g(x	NOUN
ejpam-2985	331	14	)	)	PUNCT
ejpam-2985	331	15	is	be	AUX
ejpam-2985	331	16	a	a	DET
ejpam-2985	331	17	complete	complete	ADJ
ejpam-2985	331	18	subspace	subspace	NOUN
ejpam-2985	331	19	of	of	ADP
ejpam-2985	331	20	x	x	PRON
ejpam-2985	331	21	,	,	PUNCT
ejpam-2985	331	22	then	then	ADV
ejpam-2985	331	23	the	the	DET
ejpam-2985	331	24	mappings	mapping	NOUN
ejpam-2985	331	25	s	s	PART
ejpam-2985	331	26	,	,	PUNCT
ejpam-2985	331	27	f	f	PROPN
ejpam-2985	331	28	and	and	CCONJ
ejpam-2985	331	29	g	g	PROPN
ejpam-2985	331	30	have	have	VERB
ejpam-2985	331	31	a	a	DET
ejpam-2985	331	32	unique	unique	ADJ
ejpam-2985	331	33	point	point	NOUN
ejpam-2985	331	34	of	of	ADP
ejpam-2985	331	35	coincidence	coincidence	NOUN
ejpam-2985	331	36	in	in	ADP
ejpam-2985	331	37	x.	x.	NOUN
ejpam-2985	331	38	moreover	moreover	ADV
ejpam-2985	331	39	,	,	PUNCT
ejpam-2985	331	40	if	if	SCONJ
ejpam-2985	331	41	(	(	PUNCT
ejpam-2985	331	42	s	s	X
ejpam-2985	331	43	,	,	PUNCT
ejpam-2985	331	44	g	g	NOUN
ejpam-2985	331	45	)	)	PUNCT
ejpam-2985	331	46	and	and	CCONJ
ejpam-2985	331	47	(	(	PUNCT
ejpam-2985	331	48	f	f	X
ejpam-2985	331	49	,	,	PUNCT
ejpam-2985	331	50	g	g	NOUN
ejpam-2985	331	51	)	)	PUNCT
ejpam-2985	331	52	are	be	AUX
ejpam-2985	331	53	weakly	weakly	ADV
ejpam-2985	331	54	compatible	compatible	ADJ
ejpam-2985	331	55	then	then	ADV
ejpam-2985	331	56	s	s	PROPN
ejpam-2985	331	57	,	,	PUNCT
ejpam-2985	331	58	f	f	PROPN
ejpam-2985	331	59	and	and	CCONJ
ejpam-2985	331	60	g	g	PROPN
ejpam-2985	331	61	have	have	VERB
ejpam-2985	331	62	a	a	DET
ejpam-2985	331	63	unique	unique	ADJ
ejpam-2985	331	64	common	common	ADJ
ejpam-2985	331	65	fixed	fix	VERB
ejpam-2985	331	66	point	point	NOUN
ejpam-2985	331	67	in	in	ADP
ejpam-2985	331	68	x.	x.	NOUN
ejpam-2985	331	69	proof	proof	NOUN
ejpam-2985	331	70	.	.	PUNCT
ejpam-2985	332	1	this	this	PRON
ejpam-2985	332	2	follows	follow	VERB
ejpam-2985	332	3	from	from	ADP
ejpam-2985	332	4	the	the	DET
ejpam-2985	332	5	remark	remark	NOUN
ejpam-2985	332	6	2	2	NUM
ejpam-2985	332	7	and	and	CCONJ
ejpam-2985	332	8	theorem	theorem	VERB
ejpam-2985	332	9	2	2	NUM
ejpam-2985	332	10	.	.	PUNCT
ejpam-2985	332	11	a.	a.	NOUN
ejpam-2985	332	12	auwalu	auwalu	PROPN
ejpam-2985	332	13	,	,	PUNCT
ejpam-2985	332	14	e.	e.	PROPN
ejpam-2985	332	15	hınçal	hınçal	PROPN
ejpam-2985	332	16	/	/	SYM
ejpam-2985	332	17	eur	eur	PROPN
ejpam-2985	332	18	.	.	PUNCT
ejpam-2985	333	1	j.	j.	PROPN
ejpam-2985	333	2	pure	pure	PROPN
ejpam-2985	333	3	appl	appl	PROPN
ejpam-2985	333	4	.	.	PROPN
ejpam-2985	333	5	math	math	PROPN
ejpam-2985	333	6	,	,	PUNCT
ejpam-2985	333	7	10	10	NUM
ejpam-2985	333	8	(	(	PUNCT
ejpam-2985	333	9	3	3	NUM
ejpam-2985	333	10	)	)	PUNCT
ejpam-2985	333	11	(	(	PUNCT
ejpam-2985	333	12	2017	2017	NUM
ejpam-2985	333	13	)	)	PUNCT
ejpam-2985	333	14	,	,	PUNCT
ejpam-2985	333	15	473	473	NUM
ejpam-2985	333	16	-	-	SYM
ejpam-2985	333	17	487	487	NUM
ejpam-2985	333	18	485	485	NUM
ejpam-2985	333	19	corollary	corollary	ADJ
ejpam-2985	333	20	12	12	NUM
ejpam-2985	333	21	.	.	PUNCT
ejpam-2985	334	1	(	(	PUNCT
ejpam-2985	334	2	see	see	VERB
ejpam-2985	334	3	[	[	X
ejpam-2985	334	4	3	3	NUM
ejpam-2985	334	5	]	]	PUNCT
ejpam-2985	334	6	)	)	PUNCT
ejpam-2985	334	7	let	let	VERB
ejpam-2985	334	8	(	(	PUNCT
ejpam-2985	334	9	x	x	NOUN
ejpam-2985	334	10	,	,	PUNCT
ejpam-2985	334	11	d	d	NOUN
ejpam-2985	334	12	)	)	PUNCT
ejpam-2985	334	13	be	be	AUX
ejpam-2985	334	14	a	a	DET
ejpam-2985	334	15	complete	complete	ADJ
ejpam-2985	334	16	cone	cone	NOUN
ejpam-2985	334	17	pentagonal	pentagonal	ADJ
ejpam-2985	334	18	metric	metric	ADJ
ejpam-2985	334	19	space	space	NOUN
ejpam-2985	334	20	and	and	CCONJ
ejpam-2985	334	21	p	p	NOUN
ejpam-2985	334	22	be	be	AUX
ejpam-2985	334	23	a	a	DET
ejpam-2985	334	24	normal	normal	ADJ
ejpam-2985	334	25	cone	cone	NOUN
ejpam-2985	334	26	with	with	ADP
ejpam-2985	334	27	normal	normal	ADJ
ejpam-2985	334	28	constant	constant	ADJ
ejpam-2985	334	29	k.	k.	PROPN
ejpam-2985	334	30	suppose	suppose	VERB
ejpam-2985	334	31	the	the	DET
ejpam-2985	334	32	mapping	mapping	NOUN
ejpam-2985	334	33	s	s	VERB
ejpam-2985	334	34	:	:	PUNCT
ejpam-2985	334	35	x	x	SYM
ejpam-2985	334	36	→	→	SYM
ejpam-2985	334	37	x	x	SYM
ejpam-2985	334	38	satisfies	satisfy	VERB
ejpam-2985	334	39	the	the	DET
ejpam-2985	334	40	contractive	contractive	ADJ
ejpam-2985	334	41	condition	condition	NOUN
ejpam-2985	334	42	:	:	PUNCT
ejpam-2985	334	43	d(sx	d(sx	NOUN
ejpam-2985	334	44	,	,	PUNCT
ejpam-2985	334	45	sy	sy	NOUN
ejpam-2985	334	46	)	)	PUNCT
ejpam-2985	334	47	≤	≤	NUM
ejpam-2985	335	1	λ	λ	PROPN
ejpam-2985	335	2	[	[	PUNCT
ejpam-2985	335	3	d(x	d(x	PROPN
ejpam-2985	335	4	,	,	PUNCT
ejpam-2985	335	5	sx	sx	PROPN
ejpam-2985	335	6	)	)	PUNCT
ejpam-2985	335	7	+	+	NUM
ejpam-2985	335	8	d(y	d(y	PROPN
ejpam-2985	335	9	,	,	PUNCT
ejpam-2985	335	10	sy	sy	PROPN
ejpam-2985	335	11	)	)	PUNCT
ejpam-2985	335	12	]	]	PUNCT
ejpam-2985	335	13	,	,	PUNCT
ejpam-2985	335	14	(	(	PUNCT
ejpam-2985	335	15	26	26	NUM
ejpam-2985	335	16	)	)	PUNCT
ejpam-2985	335	17	for	for	ADP
ejpam-2985	335	18	all	all	DET
ejpam-2985	335	19	x	x	NOUN
ejpam-2985	335	20	,	,	PUNCT
ejpam-2985	335	21	y	y	PROPN
ejpam-2985	335	22	∈	∈	PROPN
ejpam-2985	336	1	x	x	NOUN
ejpam-2985	336	2	,	,	PUNCT
ejpam-2985	336	3	where	where	SCONJ
ejpam-2985	336	4	λ	λ	PROPN
ejpam-2985	336	5	∈	∈	PROPN
ejpam-2985	337	1	[	[	X
ejpam-2985	337	2	0	0	NUM
ejpam-2985	337	3	,	,	PUNCT
ejpam-2985	337	4	1/2	1/2	NUM
ejpam-2985	337	5	)	)	PUNCT
ejpam-2985	337	6	.	.	PUNCT
ejpam-2985	338	1	then	then	ADV
ejpam-2985	338	2	(	(	PUNCT
ejpam-2985	338	3	i	i	NOUN
ejpam-2985	338	4	)	)	PUNCT
ejpam-2985	338	5	s	s	AUX
ejpam-2985	338	6	has	have	VERB
ejpam-2985	338	7	a	a	DET
ejpam-2985	338	8	unique	unique	ADJ
ejpam-2985	338	9	fixed	fix	VERB
ejpam-2985	338	10	point	point	NOUN
ejpam-2985	338	11	in	in	ADP
ejpam-2985	338	12	x.	x.	PROPN
ejpam-2985	338	13	(	(	PUNCT
ejpam-2985	338	14	ii	ii	PROPN
ejpam-2985	338	15	)	)	PUNCT
ejpam-2985	338	16	for	for	ADP
ejpam-2985	338	17	any	any	DET
ejpam-2985	338	18	x	x	SYM
ejpam-2985	338	19	∈	∈	PROPN
ejpam-2985	338	20	x	x	NOUN
ejpam-2985	338	21	,	,	PUNCT
ejpam-2985	338	22	the	the	DET
ejpam-2985	338	23	iterative	iterative	NOUN
ejpam-2985	338	24	sequence	sequence	NOUN
ejpam-2985	338	25	{	{	PUNCT
ejpam-2985	338	26	snx	snx	NOUN
ejpam-2985	338	27	}	}	PUNCT
ejpam-2985	338	28	converges	converge	NOUN
ejpam-2985	338	29	to	to	ADP
ejpam-2985	338	30	the	the	DET
ejpam-2985	338	31	fixed	fix	VERB
ejpam-2985	338	32	point	point	NOUN
ejpam-2985	338	33	.	.	PUNCT
ejpam-2985	339	1	proof	proof	NOUN
ejpam-2985	339	2	.	.	PUNCT
ejpam-2985	340	1	putting	put	VERB
ejpam-2985	340	2	g	g	NOUN
ejpam-2985	340	3	=	=	PUNCT
ejpam-2985	340	4	i	i	PRON
ejpam-2985	340	5	in	in	ADP
ejpam-2985	340	6	corollary	corollary	ADJ
ejpam-2985	340	7	10	10	NUM
ejpam-2985	340	8	.	.	PUNCT
ejpam-2985	341	1	this	this	PRON
ejpam-2985	341	2	completes	complete	VERB
ejpam-2985	341	3	the	the	DET
ejpam-2985	341	4	proof	proof	NOUN
ejpam-2985	341	5	.	.	PUNCT
ejpam-2985	342	1	corollary	corollary	ADJ
ejpam-2985	342	2	13	13	NUM
ejpam-2985	342	3	.	.	PUNCT
ejpam-2985	343	1	(	(	PUNCT
ejpam-2985	343	2	see	see	VERB
ejpam-2985	343	3	[	[	X
ejpam-2985	343	4	18	18	NUM
ejpam-2985	343	5	]	]	PUNCT
ejpam-2985	343	6	)	)	PUNCT
ejpam-2985	343	7	let	let	VERB
ejpam-2985	343	8	(	(	PUNCT
ejpam-2985	343	9	x	x	NOUN
ejpam-2985	343	10	,	,	PUNCT
ejpam-2985	343	11	d	d	NOUN
ejpam-2985	343	12	)	)	PUNCT
ejpam-2985	343	13	be	be	AUX
ejpam-2985	343	14	a	a	DET
ejpam-2985	343	15	cone	cone	NOUN
ejpam-2985	343	16	rectangular	rectangular	ADJ
ejpam-2985	343	17	metric	metric	ADJ
ejpam-2985	343	18	space	space	NOUN
ejpam-2985	343	19	.	.	PUNCT
ejpam-2985	344	1	suppose	suppose	VERB
ejpam-2985	344	2	the	the	DET
ejpam-2985	344	3	mappings	mapping	NOUN
ejpam-2985	344	4	s	s	PART
ejpam-2985	344	5	,	,	PUNCT
ejpam-2985	344	6	g	g	NOUN
ejpam-2985	344	7	:	:	PUNCT
ejpam-2985	344	8	x	x	SYM
ejpam-2985	344	9	→	→	PUNCT
ejpam-2985	344	10	x	x	SYM
ejpam-2985	344	11	satisfies	satisfy	VERB
ejpam-2985	344	12	the	the	DET
ejpam-2985	344	13	contractive	contractive	ADJ
ejpam-2985	344	14	condition	condition	NOUN
ejpam-2985	344	15	:	:	PUNCT
ejpam-2985	344	16	d(sx	d(sx	NOUN
ejpam-2985	344	17	,	,	PUNCT
ejpam-2985	344	18	sy	sy	NOUN
ejpam-2985	344	19	)	)	PUNCT
ejpam-2985	344	20	≤	≤	NUM
ejpam-2985	345	1	λ	λ	PROPN
ejpam-2985	345	2	[	[	PUNCT
ejpam-2985	345	3	d(gx	d(gx	PROPN
ejpam-2985	345	4	,	,	PUNCT
ejpam-2985	345	5	sx	sx	PROPN
ejpam-2985	345	6	)	)	PUNCT
ejpam-2985	345	7	+	+	NUM
ejpam-2985	345	8	d(gy	d(gy	PROPN
ejpam-2985	345	9	,	,	PUNCT
ejpam-2985	345	10	sy	sy	PROPN
ejpam-2985	345	11	)	)	PUNCT
ejpam-2985	345	12	]	]	PUNCT
ejpam-2985	345	13	,	,	PUNCT
ejpam-2985	345	14	for	for	ADP
ejpam-2985	345	15	all	all	DET
ejpam-2985	345	16	x	x	NOUN
ejpam-2985	345	17	,	,	PUNCT
ejpam-2985	345	18	y	y	PROPN
ejpam-2985	345	19	∈	∈	PROPN
ejpam-2985	345	20	x	x	NOUN
ejpam-2985	345	21	,	,	PUNCT
ejpam-2985	345	22	where	where	SCONJ
ejpam-2985	345	23	λ	λ	PROPN
ejpam-2985	345	24	∈	∈	PROPN
ejpam-2985	346	1	[	[	X
ejpam-2985	346	2	0	0	NUM
ejpam-2985	346	3	,	,	PUNCT
ejpam-2985	346	4	1/2	1/2	NUM
ejpam-2985	346	5	)	)	PUNCT
ejpam-2985	346	6	.	.	PUNCT
ejpam-2985	347	1	suppose	suppose	VERB
ejpam-2985	347	2	that	that	SCONJ
ejpam-2985	347	3	s(x	s(x	NOUN
ejpam-2985	347	4	)	)	PUNCT
ejpam-2985	347	5	⊆	⊆	NUM
ejpam-2985	347	6	g(x	g(x	NOUN
ejpam-2985	347	7	)	)	PUNCT
ejpam-2985	347	8	,	,	PUNCT
ejpam-2985	347	9	and	and	CCONJ
ejpam-2985	347	10	s(x	s(x	NOUN
ejpam-2985	347	11	)	)	PUNCT
ejpam-2985	347	12	or	or	CCONJ
ejpam-2985	347	13	g(x	g(x	NOUN
ejpam-2985	347	14	)	)	PUNCT
ejpam-2985	347	15	is	be	AUX
ejpam-2985	347	16	a	a	DET
ejpam-2985	347	17	complete	complete	ADJ
ejpam-2985	347	18	subspace	subspace	NOUN
ejpam-2985	347	19	of	of	ADP
ejpam-2985	347	20	x	x	PRON
ejpam-2985	347	21	,	,	PUNCT
ejpam-2985	347	22	then	then	ADV
ejpam-2985	347	23	the	the	DET
ejpam-2985	347	24	mappings	mapping	NOUN
ejpam-2985	347	25	s	s	PART
ejpam-2985	347	26	and	and	CCONJ
ejpam-2985	347	27	g	g	PROPN
ejpam-2985	347	28	have	have	VERB
ejpam-2985	347	29	a	a	DET
ejpam-2985	347	30	unique	unique	ADJ
ejpam-2985	347	31	point	point	NOUN
ejpam-2985	347	32	of	of	ADP
ejpam-2985	347	33	coincidence	coincidence	NOUN
ejpam-2985	347	34	in	in	ADP
ejpam-2985	347	35	x.	x.	NOUN
ejpam-2985	347	36	moreover	moreover	ADV
ejpam-2985	347	37	,	,	PUNCT
ejpam-2985	347	38	if	if	SCONJ
ejpam-2985	347	39	s	s	X
ejpam-2985	347	40	and	and	CCONJ
ejpam-2985	347	41	g	g	PROPN
ejpam-2985	347	42	are	be	AUX
ejpam-2985	347	43	weakly	weakly	ADV
ejpam-2985	347	44	compatible	compatible	ADJ
ejpam-2985	347	45	then	then	ADV
ejpam-2985	347	46	s	s	VERB
ejpam-2985	347	47	and	and	CCONJ
ejpam-2985	347	48	g	g	PROPN
ejpam-2985	347	49	have	have	VERB
ejpam-2985	347	50	a	a	DET
ejpam-2985	347	51	unique	unique	ADJ
ejpam-2985	347	52	common	common	ADJ
ejpam-2985	347	53	fixed	fix	VERB
ejpam-2985	347	54	point	point	NOUN
ejpam-2985	347	55	in	in	ADP
ejpam-2985	347	56	x.	x.	NOUN
ejpam-2985	347	57	proof	proof	NOUN
ejpam-2985	347	58	.	.	PUNCT
ejpam-2985	348	1	this	this	PRON
ejpam-2985	348	2	follows	follow	VERB
ejpam-2985	348	3	from	from	ADP
ejpam-2985	348	4	the	the	DET
ejpam-2985	348	5	remark	remark	NOUN
ejpam-2985	348	6	2	2	NUM
ejpam-2985	348	7	and	and	CCONJ
ejpam-2985	348	8	corollary	corollary	ADJ
ejpam-2985	348	9	10	10	NUM
ejpam-2985	348	10	.	.	PUNCT
ejpam-2985	349	1	corollary	corollary	ADJ
ejpam-2985	349	2	14	14	NUM
ejpam-2985	349	3	.	.	PUNCT
ejpam-2985	350	1	(	(	PUNCT
ejpam-2985	350	2	see	see	VERB
ejpam-2985	350	3	[	[	X
ejpam-2985	350	4	13	13	NUM
ejpam-2985	350	5	]	]	PUNCT
ejpam-2985	350	6	)	)	PUNCT
ejpam-2985	350	7	let	let	VERB
ejpam-2985	350	8	(	(	PUNCT
ejpam-2985	350	9	x	x	NOUN
ejpam-2985	350	10	,	,	PUNCT
ejpam-2985	350	11	d	d	NOUN
ejpam-2985	350	12	)	)	PUNCT
ejpam-2985	350	13	be	be	AUX
ejpam-2985	350	14	a	a	DET
ejpam-2985	350	15	complete	complete	ADJ
ejpam-2985	350	16	cone	cone	NOUN
ejpam-2985	350	17	rectangular	rectangular	ADJ
ejpam-2985	350	18	metric	metric	ADJ
ejpam-2985	350	19	space	space	NOUN
ejpam-2985	350	20	and	and	CCONJ
ejpam-2985	350	21	p	p	NOUN
ejpam-2985	350	22	be	be	AUX
ejpam-2985	350	23	a	a	DET
ejpam-2985	350	24	normal	normal	ADJ
ejpam-2985	350	25	cone	cone	NOUN
ejpam-2985	350	26	with	with	ADP
ejpam-2985	350	27	normal	normal	ADJ
ejpam-2985	350	28	constant	constant	ADJ
ejpam-2985	350	29	k.	k.	PROPN
ejpam-2985	350	30	suppose	suppose	VERB
ejpam-2985	350	31	the	the	DET
ejpam-2985	350	32	mapping	mapping	NOUN
ejpam-2985	350	33	s	s	VERB
ejpam-2985	350	34	:	:	PUNCT
ejpam-2985	350	35	x	x	SYM
ejpam-2985	350	36	→	→	SYM
ejpam-2985	350	37	x	x	SYM
ejpam-2985	350	38	satisfies	satisfy	VERB
ejpam-2985	350	39	the	the	DET
ejpam-2985	350	40	contractive	contractive	ADJ
ejpam-2985	350	41	condition	condition	NOUN
ejpam-2985	350	42	:	:	PUNCT
ejpam-2985	350	43	d(sx	d(sx	NOUN
ejpam-2985	350	44	,	,	PUNCT
ejpam-2985	350	45	sy	sy	NOUN
ejpam-2985	350	46	)	)	PUNCT
ejpam-2985	350	47	≤	≤	NUM
ejpam-2985	351	1	λ	λ	PROPN
ejpam-2985	351	2	[	[	PUNCT
ejpam-2985	351	3	d(x	d(x	PROPN
ejpam-2985	351	4	,	,	PUNCT
ejpam-2985	351	5	sx	sx	PROPN
ejpam-2985	351	6	)	)	PUNCT
ejpam-2985	351	7	+	+	NUM
ejpam-2985	351	8	d(y	d(y	PROPN
ejpam-2985	351	9	,	,	PUNCT
ejpam-2985	351	10	sy	sy	PROPN
ejpam-2985	351	11	)	)	PUNCT
ejpam-2985	351	12	]	]	PUNCT
ejpam-2985	351	13	,	,	PUNCT
ejpam-2985	351	14	(	(	PUNCT
ejpam-2985	351	15	27	27	NUM
ejpam-2985	351	16	)	)	PUNCT
ejpam-2985	351	17	for	for	ADP
ejpam-2985	351	18	all	all	DET
ejpam-2985	351	19	x	x	NOUN
ejpam-2985	351	20	,	,	PUNCT
ejpam-2985	351	21	y	y	PROPN
ejpam-2985	351	22	∈	∈	PROPN
ejpam-2985	352	1	x	x	NOUN
ejpam-2985	352	2	,	,	PUNCT
ejpam-2985	352	3	where	where	SCONJ
ejpam-2985	352	4	λ	λ	PROPN
ejpam-2985	352	5	∈	∈	PROPN
ejpam-2985	353	1	[	[	X
ejpam-2985	353	2	0	0	NUM
ejpam-2985	353	3	,	,	PUNCT
ejpam-2985	353	4	1/2	1/2	NUM
ejpam-2985	353	5	)	)	PUNCT
ejpam-2985	353	6	.	.	PUNCT
ejpam-2985	354	1	then	then	ADV
ejpam-2985	354	2	(	(	PUNCT
ejpam-2985	354	3	i	i	NOUN
ejpam-2985	354	4	)	)	PUNCT
ejpam-2985	354	5	s	s	AUX
ejpam-2985	354	6	has	have	VERB
ejpam-2985	354	7	a	a	DET
ejpam-2985	354	8	unique	unique	ADJ
ejpam-2985	354	9	fixed	fix	VERB
ejpam-2985	354	10	point	point	NOUN
ejpam-2985	354	11	in	in	ADP
ejpam-2985	354	12	x.	x.	PROPN
ejpam-2985	354	13	(	(	PUNCT
ejpam-2985	354	14	ii	ii	PROPN
ejpam-2985	354	15	)	)	PUNCT
ejpam-2985	354	16	for	for	ADP
ejpam-2985	354	17	any	any	DET
ejpam-2985	354	18	x	x	SYM
ejpam-2985	354	19	∈	∈	PROPN
ejpam-2985	354	20	x	x	NOUN
ejpam-2985	354	21	,	,	PUNCT
ejpam-2985	354	22	the	the	DET
ejpam-2985	354	23	iterative	iterative	NOUN
ejpam-2985	354	24	sequence	sequence	NOUN
ejpam-2985	354	25	{	{	PUNCT
ejpam-2985	354	26	snx	snx	NOUN
ejpam-2985	354	27	}	}	PUNCT
ejpam-2985	354	28	converges	converge	NOUN
ejpam-2985	354	29	to	to	ADP
ejpam-2985	354	30	the	the	DET
ejpam-2985	354	31	fixed	fix	VERB
ejpam-2985	354	32	point	point	NOUN
ejpam-2985	354	33	.	.	PUNCT
ejpam-2985	355	1	proof	proof	NOUN
ejpam-2985	355	2	.	.	PUNCT
ejpam-2985	356	1	putting	put	VERB
ejpam-2985	356	2	g	g	NOUN
ejpam-2985	356	3	=	=	PUNCT
ejpam-2985	356	4	i	i	PRON
ejpam-2985	356	5	in	in	ADP
ejpam-2985	356	6	corollary	corollary	ADJ
ejpam-2985	356	7	10	10	NUM
ejpam-2985	356	8	and	and	CCONJ
ejpam-2985	356	9	remark	remark	NOUN
ejpam-2985	356	10	2	2	NUM
ejpam-2985	356	11	.	.	PUNCT
ejpam-2985	357	1	this	this	PRON
ejpam-2985	357	2	completes	complete	VERB
ejpam-2985	357	3	the	the	DET
ejpam-2985	357	4	proof	proof	NOUN
ejpam-2985	357	5	.	.	PUNCT
ejpam-2985	358	1	example	example	NOUN
ejpam-2985	359	1	2	2	NUM
ejpam-2985	359	2	.	.	PUNCT
ejpam-2985	360	1	let	let	VERB
ejpam-2985	360	2	x	x	PUNCT
ejpam-2985	360	3	=	=	PRON
ejpam-2985	360	4	{	{	PUNCT
ejpam-2985	360	5	1	1	NUM
ejpam-2985	360	6	,	,	PUNCT
ejpam-2985	360	7	2	2	NUM
ejpam-2985	360	8	,	,	PUNCT
ejpam-2985	360	9	3	3	NUM
ejpam-2985	360	10	,	,	PUNCT
ejpam-2985	360	11	4	4	NUM
ejpam-2985	360	12	,	,	PUNCT
ejpam-2985	360	13	5	5	NUM
ejpam-2985	360	14	}	}	PUNCT
ejpam-2985	360	15	,	,	PUNCT
ejpam-2985	360	16	e	e	X
ejpam-2985	360	17	=	=	PUNCT
ejpam-2985	360	18	r2	r2	PROPN
ejpam-2985	360	19	and	and	CCONJ
ejpam-2985	360	20	p	p	NOUN
ejpam-2985	360	21	=	=	X
ejpam-2985	360	22	{	{	PUNCT
ejpam-2985	360	23	(	(	PUNCT
ejpam-2985	360	24	x	x	NOUN
ejpam-2985	360	25	,	,	PUNCT
ejpam-2985	360	26	y	y	PROPN
ejpam-2985	360	27	)	)	PUNCT
ejpam-2985	360	28	:	:	PUNCT
ejpam-2985	361	1	x	x	X
ejpam-2985	361	2	,	,	PUNCT
ejpam-2985	361	3	y	y	PROPN
ejpam-2985	361	4	≥	≥	NOUN
ejpam-2985	361	5	0	0	NUM
ejpam-2985	361	6	}	}	PUNCT
ejpam-2985	361	7	is	be	AUX
ejpam-2985	361	8	a	a	DET
ejpam-2985	361	9	cone	cone	NOUN
ejpam-2985	361	10	in	in	ADP
ejpam-2985	361	11	e.	e.	PROPN
ejpam-2985	361	12	define	define	VERB
ejpam-2985	362	1	d	d	X
ejpam-2985	362	2	:	:	PUNCT
ejpam-2985	362	3	x	x	PROPN
ejpam-2985	362	4	×x	×x	X
ejpam-2985	362	5	→	→	SYM
ejpam-2985	362	6	e	e	NOUN
ejpam-2985	362	7	as	as	SCONJ
ejpam-2985	362	8	follows	follow	VERB
ejpam-2985	362	9	:	:	PUNCT
ejpam-2985	362	10	d(x	d(x	PROPN
ejpam-2985	362	11	,	,	PUNCT
ejpam-2985	362	12	x	x	NOUN
ejpam-2985	362	13	)	)	PUNCT
ejpam-2985	362	14	=	=	PUNCT
ejpam-2985	363	1	0,∀x	0,∀x	NUM
ejpam-2985	363	2	∈	∈	PROPN
ejpam-2985	363	3	x	x	X
ejpam-2985	363	4	;	;	PUNCT
ejpam-2985	363	5	d(1	d(1	VERB
ejpam-2985	363	6	,	,	PUNCT
ejpam-2985	363	7	2	2	NUM
ejpam-2985	363	8	)	)	PUNCT
ejpam-2985	364	1	=	=	SYM
ejpam-2985	364	2	d(2	d(2	PROPN
ejpam-2985	364	3	,	,	PUNCT
ejpam-2985	364	4	1	1	NUM
ejpam-2985	364	5	)	)	PUNCT
ejpam-2985	364	6	=	=	NOUN
ejpam-2985	364	7	(	(	PUNCT
ejpam-2985	364	8	4	4	NUM
ejpam-2985	364	9	,	,	PUNCT
ejpam-2985	364	10	8)	8)	NUM
ejpam-2985	364	11	;	;	PUNCT
ejpam-2985	364	12	d(1	d(1	VERB
ejpam-2985	364	13	,	,	PUNCT
ejpam-2985	364	14	3	3	X
ejpam-2985	364	15	)	)	PUNCT
ejpam-2985	364	16	=	=	SYM
ejpam-2985	365	1	d(3	d(3	PROPN
ejpam-2985	365	2	,	,	PUNCT
ejpam-2985	365	3	1	1	NUM
ejpam-2985	365	4	)	)	PUNCT
ejpam-2985	365	5	=	=	SYM
ejpam-2985	366	1	d(3	d(3	PROPN
ejpam-2985	366	2	,	,	PUNCT
ejpam-2985	366	3	4	4	NUM
ejpam-2985	366	4	)	)	PUNCT
ejpam-2985	366	5	=	=	SYM
ejpam-2985	366	6	d(4	d(4	PROPN
ejpam-2985	366	7	,	,	PUNCT
ejpam-2985	366	8	3	3	NUM
ejpam-2985	366	9	)	)	PUNCT
ejpam-2985	366	10	=	=	SYM
ejpam-2985	367	1	d(2	d(2	PROPN
ejpam-2985	367	2	,	,	PUNCT
ejpam-2985	367	3	4	4	NUM
ejpam-2985	367	4	)	)	PUNCT
ejpam-2985	367	5	=	=	SYM
ejpam-2985	367	6	d(4	d(4	NOUN
ejpam-2985	367	7	,	,	PUNCT
ejpam-2985	367	8	2	2	NUM
ejpam-2985	367	9	)	)	PUNCT
ejpam-2985	367	10	=	=	NOUN
ejpam-2985	367	11	(	(	PUNCT
ejpam-2985	367	12	1	1	NUM
ejpam-2985	367	13	,	,	PUNCT
ejpam-2985	367	14	2	2	NUM
ejpam-2985	367	15	)	)	PUNCT
ejpam-2985	367	16	;	;	PUNCT
ejpam-2985	367	17	d(1	d(1	VERB
ejpam-2985	367	18	,	,	PUNCT
ejpam-2985	367	19	5	5	NUM
ejpam-2985	367	20	)	)	PUNCT
ejpam-2985	367	21	=	=	SYM
ejpam-2985	368	1	d(5	d(5	PROPN
ejpam-2985	368	2	,	,	PUNCT
ejpam-2985	368	3	1	1	NUM
ejpam-2985	368	4	)	)	PUNCT
ejpam-2985	368	5	=	=	SYM
ejpam-2985	369	1	d(2	d(2	PROPN
ejpam-2985	369	2	,	,	PUNCT
ejpam-2985	369	3	5	5	NUM
ejpam-2985	369	4	)	)	PUNCT
ejpam-2985	369	5	=	=	SYM
ejpam-2985	370	1	d(5	d(5	PROPN
ejpam-2985	370	2	,	,	PUNCT
ejpam-2985	370	3	2	2	NUM
ejpam-2985	370	4	)	)	PUNCT
ejpam-2985	370	5	=	=	SYM
ejpam-2985	371	1	d(3	d(3	PROPN
ejpam-2985	371	2	,	,	PUNCT
ejpam-2985	371	3	5	5	NUM
ejpam-2985	371	4	)	)	PUNCT
ejpam-2985	371	5	=	=	SYM
ejpam-2985	371	6	d(5	d(5	PROPN
ejpam-2985	371	7	,	,	PUNCT
ejpam-2985	371	8	3	3	NUM
ejpam-2985	371	9	)	)	PUNCT
ejpam-2985	371	10	=	=	SYM
ejpam-2985	371	11	d(4	d(4	NOUN
ejpam-2985	371	12	,	,	PUNCT
ejpam-2985	371	13	5	5	NUM
ejpam-2985	371	14	)	)	PUNCT
ejpam-2985	371	15	=	=	SYM
ejpam-2985	371	16	d(5	d(5	PROPN
ejpam-2985	371	17	,	,	PUNCT
ejpam-2985	371	18	4	4	NUM
ejpam-2985	371	19	)	)	PUNCT
ejpam-2985	371	20	=	=	NOUN
ejpam-2985	371	21	(	(	PUNCT
ejpam-2985	371	22	3	3	NUM
ejpam-2985	371	23	,	,	PUNCT
ejpam-2985	371	24	6	6	NUM
ejpam-2985	371	25	)	)	PUNCT
ejpam-2985	371	26	.	.	PUNCT
ejpam-2985	372	1	references	reference	NOUN
ejpam-2985	372	2	486	486	NUM
ejpam-2985	372	3	then	then	ADV
ejpam-2985	372	4	(	(	PUNCT
ejpam-2985	372	5	x	x	X
ejpam-2985	372	6	,	,	PUNCT
ejpam-2985	372	7	d	d	NOUN
ejpam-2985	372	8	)	)	PUNCT
ejpam-2985	372	9	is	be	AUX
ejpam-2985	372	10	a	a	DET
ejpam-2985	372	11	cone	cone	NOUN
ejpam-2985	372	12	pentagonal	pentagonal	ADJ
ejpam-2985	372	13	metric	metric	ADJ
ejpam-2985	372	14	space	space	NOUN
ejpam-2985	372	15	,	,	PUNCT
ejpam-2985	372	16	but	but	CCONJ
ejpam-2985	372	17	(	(	PUNCT
ejpam-2985	372	18	x	x	X
ejpam-2985	372	19	,	,	PUNCT
ejpam-2985	372	20	d	d	NOUN
ejpam-2985	372	21	)	)	PUNCT
ejpam-2985	372	22	is	be	AUX
ejpam-2985	372	23	not	not	PART
ejpam-2985	372	24	a	a	DET
ejpam-2985	372	25	cone	cone	NOUN
ejpam-2985	372	26	rectangular	rectangular	ADJ
ejpam-2985	372	27	metric	metric	ADJ
ejpam-2985	372	28	space	space	NOUN
ejpam-2985	372	29	because	because	SCONJ
ejpam-2985	372	30	it	it	PRON
ejpam-2985	372	31	lacks	lack	VERB
ejpam-2985	372	32	the	the	DET
ejpam-2985	372	33	rectangular	rectangular	ADJ
ejpam-2985	372	34	property	property	NOUN
ejpam-2985	372	35	:	:	PUNCT
ejpam-2985	372	36	(	(	PUNCT
ejpam-2985	372	37	4	4	NUM
ejpam-2985	372	38	,	,	PUNCT
ejpam-2985	372	39	8)	8)	NUM
ejpam-2985	372	40	=	=	SYM
ejpam-2985	372	41	d(1	d(1	PROPN
ejpam-2985	372	42	,	,	PUNCT
ejpam-2985	372	43	2	2	NUM
ejpam-2985	372	44	)	)	PUNCT
ejpam-2985	372	45	>	>	X
ejpam-2985	373	1	d(1	d(1	PROPN
ejpam-2985	373	2	,	,	PUNCT
ejpam-2985	373	3	3	3	NUM
ejpam-2985	373	4	)	)	PUNCT
ejpam-2985	373	5	+	+	CCONJ
ejpam-2985	374	1	d(3	d(3	PROPN
ejpam-2985	374	2	,	,	PUNCT
ejpam-2985	374	3	4	4	NUM
ejpam-2985	374	4	)	)	PUNCT
ejpam-2985	374	5	+	+	CCONJ
ejpam-2985	374	6	d(4	d(4	NOUN
ejpam-2985	374	7	,	,	PUNCT
ejpam-2985	374	8	2	2	NUM
ejpam-2985	374	9	)	)	PUNCT
ejpam-2985	374	10	=	=	NOUN
ejpam-2985	374	11	(	(	PUNCT
ejpam-2985	374	12	1	1	NUM
ejpam-2985	374	13	,	,	PUNCT
ejpam-2985	374	14	2	2	NUM
ejpam-2985	374	15	)	)	PUNCT
ejpam-2985	374	16	+	+	CCONJ
ejpam-2985	374	17	(	(	PUNCT
ejpam-2985	374	18	1	1	NUM
ejpam-2985	374	19	,	,	PUNCT
ejpam-2985	374	20	2	2	NUM
ejpam-2985	374	21	)	)	PUNCT
ejpam-2985	374	22	+	+	CCONJ
ejpam-2985	374	23	(	(	PUNCT
ejpam-2985	374	24	1	1	NUM
ejpam-2985	374	25	,	,	PUNCT
ejpam-2985	374	26	2	2	NUM
ejpam-2985	374	27	)	)	PUNCT
ejpam-2985	374	28	=	=	NOUN
ejpam-2985	374	29	(	(	PUNCT
ejpam-2985	374	30	3	3	NUM
ejpam-2985	374	31	,	,	PUNCT
ejpam-2985	374	32	6	6	NUM
ejpam-2985	374	33	)	)	PUNCT
ejpam-2985	374	34	as	as	ADP
ejpam-2985	374	35	(	(	PUNCT
ejpam-2985	374	36	4	4	NUM
ejpam-2985	374	37	,	,	PUNCT
ejpam-2985	374	38	8)−	8)−	NUM
ejpam-2985	374	39	(	(	PUNCT
ejpam-2985	374	40	3	3	NUM
ejpam-2985	374	41	,	,	PUNCT
ejpam-2985	374	42	6	6	NUM
ejpam-2985	374	43	)	)	PUNCT
ejpam-2985	374	44	=	=	SYM
ejpam-2985	374	45	(	(	PUNCT
ejpam-2985	374	46	1	1	NUM
ejpam-2985	374	47	,	,	PUNCT
ejpam-2985	374	48	2	2	NUM
ejpam-2985	374	49	)	)	PUNCT
ejpam-2985	374	50	∈	∈	PROPN
ejpam-2985	374	51	p.	p.	NOUN
ejpam-2985	374	52	define	define	VERB
ejpam-2985	374	53	a	a	DET
ejpam-2985	374	54	mapping	mapping	NOUN
ejpam-2985	374	55	s	s	NOUN
ejpam-2985	374	56	,	,	PUNCT
ejpam-2985	374	57	f	f	PROPN
ejpam-2985	374	58	and	and	CCONJ
ejpam-2985	374	59	g	g	PROPN
ejpam-2985	374	60	:	:	PUNCT
ejpam-2985	374	61	x	x	SYM
ejpam-2985	374	62	→	→	SYM
ejpam-2985	374	63	x	x	PUNCT
ejpam-2985	374	64	as	as	SCONJ
ejpam-2985	374	65	follows	follow	VERB
ejpam-2985	374	66	:	:	PUNCT
ejpam-2985	374	67	s(x	s(x	X
ejpam-2985	374	68	)	)	PUNCT
ejpam-2985	374	69	=	=	SYM
ejpam-2985	375	1	4	4	NUM
ejpam-2985	375	2	,	,	PUNCT
ejpam-2985	375	3	∀x	∀x	X
ejpam-2985	375	4	∈	∈	PROPN
ejpam-2985	375	5	x.	x.	NOUN
ejpam-2985	375	6	f(x	f(x	PROPN
ejpam-2985	375	7	)	)	PUNCT
ejpam-2985	376	1	=	=	PRON
ejpam-2985	376	2	{	{	PUNCT
ejpam-2985	376	3	4	4	NUM
ejpam-2985	376	4	,	,	PUNCT
ejpam-2985	376	5	if	if	SCONJ
ejpam-2985	376	6	x	x	SYM
ejpam-2985	376	7	6=	6=	ADP
ejpam-2985	376	8	5	5	NUM
ejpam-2985	376	9	;	;	PUNCT
ejpam-2985	376	10	2	2	NUM
ejpam-2985	376	11	,	,	PUNCT
ejpam-2985	376	12	if	if	SCONJ
ejpam-2985	376	13	x	x	X
ejpam-2985	376	14	=	=	SYM
ejpam-2985	376	15	5	5	NUM
ejpam-2985	376	16	.	.	PUNCT
ejpam-2985	376	17	g(x	g(x	NOUN
ejpam-2985	376	18	)	)	PUNCT
ejpam-2985	377	1	=	=	PUNCT
ejpam-2985	377	2			NOUN
ejpam-2985	377	3	3	3	NUM
ejpam-2985	377	4	,	,	PUNCT
ejpam-2985	377	5	if	if	SCONJ
ejpam-2985	377	6	x	x	ADP
ejpam-2985	377	7	=	=	SYM
ejpam-2985	377	8	1	1	NUM
ejpam-2985	377	9	;	;	PUNCT
ejpam-2985	377	10	1	1	NUM
ejpam-2985	377	11	,	,	PUNCT
ejpam-2985	377	12	if	if	SCONJ
ejpam-2985	377	13	x	x	ADP
ejpam-2985	377	14	=	=	SYM
ejpam-2985	377	15	2	2	NUM
ejpam-2985	377	16	;	;	PUNCT
ejpam-2985	377	17	2	2	NUM
ejpam-2985	377	18	,	,	PUNCT
ejpam-2985	377	19	if	if	SCONJ
ejpam-2985	377	20	x	x	PROPN
ejpam-2985	377	21	=	=	SYM
ejpam-2985	377	22	3	3	NUM
ejpam-2985	377	23	;	;	PUNCT
ejpam-2985	377	24	4	4	NUM
ejpam-2985	377	25	,	,	PUNCT
ejpam-2985	377	26	if	if	SCONJ
ejpam-2985	377	27	x	x	X
ejpam-2985	377	28	=	=	SYM
ejpam-2985	377	29	4	4	NUM
ejpam-2985	377	30	;	;	PUNCT
ejpam-2985	377	31	5	5	NUM
ejpam-2985	377	32	,	,	PUNCT
ejpam-2985	377	33	if	if	SCONJ
ejpam-2985	377	34	x	x	ADP
ejpam-2985	377	35	=	=	SYM
ejpam-2985	377	36	5	5	X
ejpam-2985	377	37	.	.	PUNCT
ejpam-2985	377	38	clearly	clearly	ADV
ejpam-2985	377	39	s(x)∪	s(x)∪	VERB
ejpam-2985	377	40	f(x	f(x	PROPN
ejpam-2985	377	41	)	)	PUNCT
ejpam-2985	377	42	⊆	⊆	NUM
ejpam-2985	377	43	g(x	g(x	NOUN
ejpam-2985	377	44	)	)	PUNCT
ejpam-2985	377	45	,	,	PUNCT
ejpam-2985	377	46	g(x	g(x	NOUN
ejpam-2985	377	47	)	)	PUNCT
ejpam-2985	377	48	is	be	AUX
ejpam-2985	377	49	a	a	DET
ejpam-2985	377	50	complete	complete	ADJ
ejpam-2985	377	51	subspace	subspace	NOUN
ejpam-2985	377	52	of	of	ADP
ejpam-2985	377	53	x.	x.	NOUN
ejpam-2985	377	54	also	also	ADV
ejpam-2985	377	55	,	,	PUNCT
ejpam-2985	377	56	the	the	DET
ejpam-2985	377	57	pairs	pair	NOUN
ejpam-2985	377	58	(	(	PUNCT
ejpam-2985	377	59	s	s	X
ejpam-2985	377	60	,	,	PUNCT
ejpam-2985	377	61	g	g	NOUN
ejpam-2985	377	62	)	)	PUNCT
ejpam-2985	377	63	and	and	CCONJ
ejpam-2985	377	64	(	(	PUNCT
ejpam-2985	377	65	f	f	X
ejpam-2985	377	66	,	,	PUNCT
ejpam-2985	377	67	g	g	NOUN
ejpam-2985	377	68	)	)	PUNCT
ejpam-2985	377	69	are	be	AUX
ejpam-2985	377	70	weakly	weakly	ADJ
ejpam-2985	377	71	compatibles	compatible	NOUN
ejpam-2985	377	72	.	.	PUNCT
ejpam-2985	378	1	the	the	DET
ejpam-2985	378	2	conditions	condition	NOUN
ejpam-2985	378	3	of	of	ADP
ejpam-2985	378	4	theorem	theorem	ADJ
ejpam-2985	378	5	2	2	NUM
ejpam-2985	378	6	holds	hold	VERB
ejpam-2985	378	7	for	for	ADP
ejpam-2985	378	8	all	all	DET
ejpam-2985	378	9	x	x	NOUN
ejpam-2985	378	10	,	,	PUNCT
ejpam-2985	378	11	y	y	PROPN
ejpam-2985	378	12	∈	∈	PROPN
ejpam-2985	378	13	x	x	NOUN
ejpam-2985	378	14	,	,	PUNCT
ejpam-2985	378	15	where	where	SCONJ
ejpam-2985	378	16	λ	λ	X
ejpam-2985	378	17	=	=	NOUN
ejpam-2985	378	18	1	1	NUM
ejpam-2985	378	19	3	3	NUM
ejpam-2985	378	20	,	,	PUNCT
ejpam-2985	378	21	and	and	CCONJ
ejpam-2985	378	22	4	4	NUM
ejpam-2985	378	23	is	be	AUX
ejpam-2985	378	24	the	the	DET
ejpam-2985	378	25	unique	unique	ADJ
ejpam-2985	378	26	common	common	ADJ
ejpam-2985	378	27	fixed	fix	VERB
ejpam-2985	378	28	point	point	NOUN
ejpam-2985	378	29	of	of	ADP
ejpam-2985	378	30	the	the	DET
ejpam-2985	378	31	mappings	mapping	NOUN
ejpam-2985	378	32	s	s	PART
ejpam-2985	378	33	,	,	PUNCT
ejpam-2985	378	34	f	f	PROPN
ejpam-2985	378	35	and	and	CCONJ
ejpam-2985	378	36	g.	g.	PROPN
ejpam-2985	378	37	acknowledgements	acknowledgement	NOUN
ejpam-2985	378	38	this	this	DET
ejpam-2985	378	39	research	research	NOUN
ejpam-2985	378	40	project	project	NOUN
ejpam-2985	378	41	was	be	AUX
ejpam-2985	378	42	supported	support	VERB
ejpam-2985	378	43	by	by	ADP
ejpam-2985	378	44	the	the	DET
ejpam-2985	378	45	center	center	NOUN
ejpam-2985	378	46	of	of	ADP
ejpam-2985	378	47	excellence	excellence	NOUN
ejpam-2985	378	48	,	,	PUNCT
ejpam-2985	378	49	near	near	ADP
ejpam-2985	378	50	east	east	PROPN
ejpam-2985	378	51	university	university	PROPN
ejpam-2985	378	52	,	,	PUNCT
ejpam-2985	378	53	nicosia	nicosia	NOUN
ejpam-2985	378	54	-	-	PUNCT
ejpam-2985	378	55	trnc	trnc	PROPN
ejpam-2985	378	56	,	,	PUNCT
ejpam-2985	378	57	mersin	mersin	PROPN
ejpam-2985	378	58	10	10	NUM
ejpam-2985	378	59	,	,	PUNCT
ejpam-2985	378	60	turkey	turkey	NOUN
ejpam-2985	378	61	.	.	PUNCT
ejpam-2985	379	1	references	reference	NOUN
ejpam-2985	379	2	[	[	X
ejpam-2985	379	3	1	1	NUM
ejpam-2985	379	4	]	]	X
ejpam-2985	379	5	m	m	VERB
ejpam-2985	379	6	abbas	abbas	NOUN
ejpam-2985	379	7	and	and	CCONJ
ejpam-2985	379	8	g	g	PROPN
ejpam-2985	379	9	jungck	jungck	NOUN
ejpam-2985	379	10	.	.	PUNCT
ejpam-2985	380	1	common	common	ADJ
ejpam-2985	380	2	fixed	fix	VERB
ejpam-2985	380	3	point	point	NOUN
ejpam-2985	380	4	results	result	NOUN
ejpam-2985	380	5	for	for	ADP
ejpam-2985	380	6	non	non	ADJ
ejpam-2985	380	7	commuting	commuting	NOUN
ejpam-2985	380	8	mappings	mapping	NOUN
ejpam-2985	380	9	without	without	ADP
ejpam-2985	380	10	continuity	continuity	NOUN
ejpam-2985	380	11	in	in	ADP
ejpam-2985	380	12	cone	cone	NOUN
ejpam-2985	380	13	metric	metric	ADJ
ejpam-2985	380	14	spaces	space	NOUN
ejpam-2985	380	15	.	.	PUNCT
ejpam-2985	381	1	journal	journal	PROPN
ejpam-2985	381	2	of	of	ADP
ejpam-2985	381	3	mathematical	mathematical	ADJ
ejpam-2985	381	4	analysis	analysis	NOUN
ejpam-2985	381	5	and	and	CCONJ
ejpam-2985	381	6	applications	application	NOUN
ejpam-2985	381	7	,	,	PUNCT
ejpam-2985	381	8	341(1):416–420	341(1):416–420	NUM
ejpam-2985	381	9	,	,	PUNCT
ejpam-2985	381	10	2008	2008	NUM
ejpam-2985	381	11	.	.	PUNCT
ejpam-2985	382	1	[	[	X
ejpam-2985	382	2	2	2	X
ejpam-2985	382	3	]	]	PUNCT
ejpam-2985	382	4	a	a	DET
ejpam-2985	382	5	auwalu	auwalu	NOUN
ejpam-2985	382	6	.	.	PUNCT
ejpam-2985	383	1	banach	banach	ADV
ejpam-2985	383	2	fixed	fix	VERB
ejpam-2985	383	3	point	point	NOUN
ejpam-2985	383	4	theorem	theorem	VERB
ejpam-2985	383	5	in	in	ADP
ejpam-2985	383	6	a	a	DET
ejpam-2985	383	7	cone	cone	NOUN
ejpam-2985	383	8	pentagonal	pentagonal	ADJ
ejpam-2985	383	9	metric	metric	ADJ
ejpam-2985	383	10	spaces	space	NOUN
ejpam-2985	383	11	.	.	PUNCT
ejpam-2985	384	1	journal	journal	NOUN
ejpam-2985	384	2	of	of	ADP
ejpam-2985	384	3	advanced	advanced	ADJ
ejpam-2985	384	4	studies	study	NOUN
ejpam-2985	384	5	in	in	ADP
ejpam-2985	384	6	topology	topology	NOUN
ejpam-2985	384	7	,	,	PUNCT
ejpam-2985	384	8	7(2):60–67	7(2):60–67	NUM
ejpam-2985	384	9	,	,	PUNCT
ejpam-2985	384	10	2016	2016	NUM
ejpam-2985	384	11	.	.	PUNCT
ejpam-2985	385	1	[	[	X
ejpam-2985	385	2	3	3	X
ejpam-2985	385	3	]	]	X
ejpam-2985	385	4	a	a	DET
ejpam-2985	385	5	auwalu	auwalu	NOUN
ejpam-2985	385	6	.	.	PUNCT
ejpam-2985	386	1	kannan	kannan	PROPN
ejpam-2985	386	2	fixed	fix	VERB
ejpam-2985	386	3	point	point	NOUN
ejpam-2985	386	4	theorem	theorem	VERB
ejpam-2985	386	5	in	in	ADP
ejpam-2985	386	6	a	a	DET
ejpam-2985	386	7	cone	cone	NOUN
ejpam-2985	386	8	pentagonal	pentagonal	ADJ
ejpam-2985	386	9	metric	metric	ADJ
ejpam-2985	386	10	spaces	space	NOUN
ejpam-2985	386	11	.	.	PUNCT
ejpam-2985	387	1	journal	journal	NOUN
ejpam-2985	387	2	of	of	ADP
ejpam-2985	387	3	mathematics	mathematic	NOUN
ejpam-2985	387	4	and	and	CCONJ
ejpam-2985	387	5	computational	computational	ADJ
ejpam-2985	387	6	sciences	science	NOUN
ejpam-2985	387	7	,	,	PUNCT
ejpam-2985	387	8	6(4):515–526	6(4):515–526	NOUN
ejpam-2985	387	9	,	,	PUNCT
ejpam-2985	387	10	2016	2016	NUM
ejpam-2985	387	11	.	.	PUNCT
ejpam-2985	388	1	[	[	X
ejpam-2985	388	2	4	4	X
ejpam-2985	388	3	]	]	X
ejpam-2985	388	4	a	a	DET
ejpam-2985	388	5	auwalu	auwalu	NOUN
ejpam-2985	388	6	and	and	CCONJ
ejpam-2985	388	7	e	e	NOUN
ejpam-2985	388	8	hınçal	hınçal	NOUN
ejpam-2985	388	9	.	.	PUNCT
ejpam-2985	389	1	common	common	ADJ
ejpam-2985	389	2	fixed	fix	VERB
ejpam-2985	389	3	points	point	NOUN
ejpam-2985	389	4	of	of	ADP
ejpam-2985	389	5	two	two	NUM
ejpam-2985	389	6	maps	map	NOUN
ejpam-2985	389	7	in	in	ADP
ejpam-2985	389	8	cone	cone	NOUN
ejpam-2985	389	9	pentagonal	pentagonal	ADJ
ejpam-2985	389	10	metric	metric	ADJ
ejpam-2985	389	11	spaces	space	NOUN
ejpam-2985	389	12	.	.	PUNCT
ejpam-2985	390	1	global	global	ADJ
ejpam-2985	390	2	journal	journal	PROPN
ejpam-2985	390	3	of	of	ADP
ejpam-2985	390	4	pure	pure	ADJ
ejpam-2985	390	5	and	and	CCONJ
ejpam-2985	390	6	applied	applied	ADJ
ejpam-2985	390	7	mathematics	mathematic	NOUN
ejpam-2985	390	8	,	,	PUNCT
ejpam-2985	390	9	12(3):2423–2435	12(3):2423–2435	NUM
ejpam-2985	390	10	,	,	PUNCT
ejpam-2985	390	11	2016	2016	NUM
ejpam-2985	390	12	.	.	PUNCT
ejpam-2985	391	1	references	reference	NOUN
ejpam-2985	391	2	487	487	NUM
ejpam-2985	392	1	[	[	X
ejpam-2985	392	2	5	5	NUM
ejpam-2985	392	3	]	]	PUNCT
ejpam-2985	392	4	a	a	DET
ejpam-2985	392	5	auwalu	auwalu	NOUN
ejpam-2985	392	6	and	and	CCONJ
ejpam-2985	392	7	e	e	NOUN
ejpam-2985	392	8	hınçal	hınçal	NOUN
ejpam-2985	392	9	.	.	PUNCT
ejpam-2985	393	1	kannan	kannan	PROPN
ejpam-2985	393	2	type	type	NOUN
ejpam-2985	393	3	fixed	fix	VERB
ejpam-2985	393	4	point	point	NOUN
ejpam-2985	393	5	theorem	theorem	VERB
ejpam-2985	393	6	in	in	ADP
ejpam-2985	393	7	cone	cone	NOUN
ejpam-2985	393	8	pentagonal	pentagonal	ADJ
ejpam-2985	393	9	metric	metric	ADJ
ejpam-2985	393	10	spaces	space	NOUN
ejpam-2985	393	11	.	.	PUNCT
ejpam-2985	394	1	international	international	ADJ
ejpam-2985	394	2	jounal	jounal	NOUN
ejpam-2985	394	3	of	of	ADP
ejpam-2985	394	4	pure	pure	ADJ
ejpam-2985	394	5	and	and	CCONJ
ejpam-2985	394	6	applied	applied	ADJ
ejpam-2985	394	7	mathematics	mathematic	NOUN
ejpam-2985	394	8	,	,	PUNCT
ejpam-2985	394	9	108(1):29–38	108(1):29–38	NUM
ejpam-2985	394	10	,	,	PUNCT
ejpam-2985	394	11	2016	2016	NUM
ejpam-2985	394	12	.	.	PUNCT
ejpam-2985	395	1	[	[	X
ejpam-2985	395	2	6	6	NUM
ejpam-2985	395	3	]	]	PUNCT
ejpam-2985	395	4	a	a	DET
ejpam-2985	395	5	azam	azam	PROPN
ejpam-2985	395	6	,	,	PUNCT
ejpam-2985	395	7	m	m	VERB
ejpam-2985	395	8	m	m	VERB
ejpam-2985	395	9	arshad	arshad	ADJ
ejpam-2985	395	10	,	,	PUNCT
ejpam-2985	395	11	and	and	CCONJ
ejpam-2985	395	12	i	i	PRON
ejpam-2985	395	13	beg	beg	VERB
ejpam-2985	395	14	.	.	PUNCT
ejpam-2985	396	1	banach	banach	NOUN
ejpam-2985	396	2	contraction	contraction	NOUN
ejpam-2985	396	3	principle	principle	NOUN
ejpam-2985	396	4	on	on	ADP
ejpam-2985	396	5	cone	cone	NOUN
ejpam-2985	396	6	rectangular	rectangular	ADJ
ejpam-2985	396	7	metric	metric	ADJ
ejpam-2985	396	8	spaces	space	NOUN
ejpam-2985	396	9	.	.	PUNCT
ejpam-2985	397	1	applicable	applicable	ADJ
ejpam-2985	397	2	analysis	analysis	NOUN
ejpam-2985	397	3	and	and	CCONJ
ejpam-2985	397	4	discrete	discrete	ADJ
ejpam-2985	397	5	mathematics	mathematic	NOUN
ejpam-2985	397	6	,	,	PUNCT
ejpam-2985	397	7	3(2):236–241	3(2):236–241	NUM
ejpam-2985	397	8	,	,	PUNCT
ejpam-2985	397	9	2009	2009	NUM
ejpam-2985	397	10	.	.	PUNCT
ejpam-2985	398	1	[	[	X
ejpam-2985	398	2	7	7	NUM
ejpam-2985	398	3	]	]	X
ejpam-2985	398	4	s	s	VERB
ejpam-2985	398	5	banach	banach	NOUN
ejpam-2985	398	6	.	.	PUNCT
ejpam-2985	399	1	sur	sur	PROPN
ejpam-2985	399	2	les	les	X
ejpam-2985	399	3	opérations	opération	NOUN
ejpam-2985	399	4	dans	dan	NOUN
ejpam-2985	399	5	les	les	X
ejpam-2985	399	6	ensembles	ensemble	NOUN
ejpam-2985	399	7	abstraits	abstrait	NOUN
ejpam-2985	399	8	et	et	PROPN
ejpam-2985	399	9	leur	leur	X
ejpam-2985	399	10	application	application	PROPN
ejpam-2985	399	11	aux	aux	PROPN
ejpam-2985	399	12	équations	équations	PROPN
ejpam-2985	399	13	intégrales	intégrale	NOUN
ejpam-2985	399	14	.	.	PUNCT
ejpam-2985	400	1	fundamenta	fundamenta	PROPN
ejpam-2985	400	2	mathematicae	mathematicae	PROPN
ejpam-2985	400	3	,	,	PUNCT
ejpam-2985	400	4	3:133–181	3:133–181	NUM
ejpam-2985	400	5	,	,	PUNCT
ejpam-2985	400	6	1922	1922	NUM
ejpam-2985	400	7	.	.	PUNCT
ejpam-2985	401	1	[	[	X
ejpam-2985	401	2	8	8	NUM
ejpam-2985	401	3	]	]	X
ejpam-2985	401	4	m	m	VERB
ejpam-2985	401	5	fŕechet	fŕechet	PROPN
ejpam-2985	401	6	.	.	PUNCT
ejpam-2985	401	7	sur	sur	PROPN
ejpam-2985	401	8	quelques	quelques	PROPN
ejpam-2985	401	9	points	point	NOUN
ejpam-2985	401	10	du	du	PROPN
ejpam-2985	401	11	calcul	calcul	PROPN
ejpam-2985	401	12	fonctionnel	fonctionnel	PROPN
ejpam-2985	401	13	.	.	PUNCT
ejpam-2985	402	1	rendiconti	rendiconti	PROPN
ejpam-2985	402	2	del	del	PROPN
ejpam-2985	402	3	circolo	circolo	PROPN
ejpam-2985	402	4	matematico	matematico	NOUN
ejpam-2985	402	5	di	di	NOUN
ejpam-2985	402	6	palermo	palermo	NOUN
ejpam-2985	402	7	,	,	PUNCT
ejpam-2985	402	8	22:1–74	22:1–74	NUM
ejpam-2985	402	9	,	,	PUNCT
ejpam-2985	402	10	1906	1906	NUM
ejpam-2985	402	11	.	.	PUNCT
ejpam-2985	403	1	[	[	X
ejpam-2985	403	2	9	9	NUM
ejpam-2985	403	3	]	]	SYM
ejpam-2985	403	4	m	m	VERB
ejpam-2985	403	5	garg	garg	NOUN
ejpam-2985	403	6	and	and	CCONJ
ejpam-2985	403	7	s	s	PROPN
ejpam-2985	403	8	agarwal	agarwal	PROPN
ejpam-2985	403	9	.	.	PUNCT
ejpam-2985	404	1	banach	banach	NOUN
ejpam-2985	404	2	contraction	contraction	NOUN
ejpam-2985	404	3	principle	principle	NOUN
ejpam-2985	404	4	on	on	ADP
ejpam-2985	404	5	cone	cone	NOUN
ejpam-2985	404	6	pentagonal	pentagonal	ADJ
ejpam-2985	404	7	metric	metric	ADJ
ejpam-2985	404	8	space	space	NOUN
ejpam-2985	404	9	.	.	PUNCT
ejpam-2985	405	1	journal	journal	PROPN
ejpam-2985	405	2	of	of	ADP
ejpam-2985	405	3	advanced	advanced	ADJ
ejpam-2985	405	4	studies	study	NOUN
ejpam-2985	405	5	in	in	ADP
ejpam-2985	405	6	topology	topology	NOUN
ejpam-2985	405	7	,	,	PUNCT
ejpam-2985	405	8	3(1):12–18	3(1):12–18	NUM
ejpam-2985	405	9	,	,	PUNCT
ejpam-2985	405	10	2012	2012	NUM
ejpam-2985	405	11	.	.	PUNCT
ejpam-2985	406	1	[	[	X
ejpam-2985	406	2	10	10	NUM
ejpam-2985	406	3	]	]	X
ejpam-2985	406	4	r	r	NOUN
ejpam-2985	406	5	george	george	PROPN
ejpam-2985	406	6	,	,	PUNCT
ejpam-2985	406	7	s	s	PART
ejpam-2985	406	8	janković	janković	ADJ
ejpam-2985	406	9	,	,	PUNCT
ejpam-2985	406	10	k	k	PROPN
ejpam-2985	406	11	reshma	reshma	PROPN
ejpam-2985	406	12	,	,	PUNCT
ejpam-2985	406	13	and	and	CCONJ
ejpam-2985	406	14	s	s	VERB
ejpam-2985	406	15	shukla	shukla	NOUN
ejpam-2985	406	16	.	.	PUNCT
ejpam-2985	407	1	rectangular	rectangular	ADJ
ejpam-2985	407	2	b	b	X
ejpam-2985	407	3	-	-	PUNCT
ejpam-2985	407	4	metric	metric	ADJ
ejpam-2985	407	5	space	space	NOUN
ejpam-2985	407	6	and	and	CCONJ
ejpam-2985	407	7	contraction	contraction	NOUN
ejpam-2985	407	8	principles	principle	NOUN
ejpam-2985	407	9	.	.	PUNCT
ejpam-2985	408	1	journal	journal	PROPN
ejpam-2985	408	2	of	of	ADP
ejpam-2985	408	3	nonlinear	nonlinear	PROPN
ejpam-2985	408	4	scienceand	scienceand	NOUN
ejpam-2985	408	5	applications	application	NOUN
ejpam-2985	408	6	,	,	PUNCT
ejpam-2985	408	7	8(6):1005–1013	8(6):1005–1013	NUM
ejpam-2985	408	8	,	,	PUNCT
ejpam-2985	408	9	2015	2015	NUM
ejpam-2985	408	10	.	.	PUNCT
ejpam-2985	409	1	[	[	X
ejpam-2985	409	2	11	11	NUM
ejpam-2985	409	3	]	]	PUNCT
ejpam-2985	409	4	l	l	PROPN
ejpam-2985	409	5	huang	huang	PROPN
ejpam-2985	409	6	and	and	CCONJ
ejpam-2985	409	7	x	x	PROPN
ejpam-2985	409	8	zhang	zhang	PROPN
ejpam-2985	409	9	.	.	PUNCT
ejpam-2985	410	1	cone	cone	PROPN
ejpam-2985	410	2	metric	metric	ADJ
ejpam-2985	410	3	spaces	space	NOUN
ejpam-2985	410	4	and	and	CCONJ
ejpam-2985	410	5	fixed	fix	VERB
ejpam-2985	410	6	point	point	NOUN
ejpam-2985	410	7	theorems	theorem	NOUN
ejpam-2985	410	8	of	of	ADP
ejpam-2985	410	9	contractive	contractive	ADJ
ejpam-2985	410	10	mappings	mapping	NOUN
ejpam-2985	410	11	.	.	PUNCT
ejpam-2985	411	1	journal	journal	PROPN
ejpam-2985	411	2	of	of	ADP
ejpam-2985	411	3	mathematical	mathematical	ADJ
ejpam-2985	411	4	analysis	analysis	NOUN
ejpam-2985	411	5	and	and	CCONJ
ejpam-2985	411	6	applications	application	NOUN
ejpam-2985	411	7	,	,	PUNCT
ejpam-2985	411	8	332(2):1468–1476	332(2):1468–1476	PROPN
ejpam-2985	411	9	,	,	PUNCT
ejpam-2985	411	10	2007	2007	NUM
ejpam-2985	411	11	.	.	PUNCT
ejpam-2985	412	1	[	[	X
ejpam-2985	412	2	12	12	NUM
ejpam-2985	412	3	]	]	X
ejpam-2985	412	4	d	d	X
ejpam-2985	412	5	ilić	ilić	NOUN
ejpam-2985	412	6	and	and	CCONJ
ejpam-2985	412	7	v	v	ADP
ejpam-2985	412	8	rakoćević.	rakoćević.	PROPN
ejpam-2985	412	9	common	common	ADJ
ejpam-2985	412	10	fixed	fix	VERB
ejpam-2985	412	11	points	point	NOUN
ejpam-2985	412	12	for	for	ADP
ejpam-2985	412	13	maps	map	NOUN
ejpam-2985	412	14	on	on	ADP
ejpam-2985	412	15	cone	cone	NOUN
ejpam-2985	412	16	metric	metric	ADJ
ejpam-2985	412	17	space	space	NOUN
ejpam-2985	412	18	.	.	PUNCT
ejpam-2985	413	1	journal	journal	PROPN
ejpam-2985	413	2	of	of	ADP
ejpam-2985	413	3	mathematical	mathematical	ADJ
ejpam-2985	413	4	analysis	analysis	NOUN
ejpam-2985	413	5	and	and	CCONJ
ejpam-2985	413	6	applications	application	NOUN
ejpam-2985	413	7	,	,	PUNCT
ejpam-2985	413	8	341(2):876–882	341(2):876–882	NUM
ejpam-2985	413	9	,	,	PUNCT
ejpam-2985	413	10	2008	2008	NUM
ejpam-2985	413	11	.	.	PUNCT
ejpam-2985	414	1	[	[	X
ejpam-2985	414	2	13	13	NUM
ejpam-2985	414	3	]	]	SYM
ejpam-2985	414	4	m	m	VERB
ejpam-2985	414	5	jleli	jleli	ADJ
ejpam-2985	414	6	and	and	CCONJ
ejpam-2985	414	7	b	b	NOUN
ejpam-2985	414	8	samet	samet	NOUN
ejpam-2985	414	9	.	.	PUNCT
ejpam-2985	415	1	the	the	DET
ejpam-2985	415	2	kannans	kannan	NOUN
ejpam-2985	415	3	fixed	fix	VERB
ejpam-2985	415	4	point	point	NOUN
ejpam-2985	415	5	theorem	theorem	VERB
ejpam-2985	415	6	in	in	ADP
ejpam-2985	415	7	a	a	DET
ejpam-2985	415	8	cone	cone	NOUN
ejpam-2985	415	9	rectangular	rectangular	ADJ
ejpam-2985	415	10	metric	metric	ADJ
ejpam-2985	415	11	space	space	NOUN
ejpam-2985	415	12	.	.	PUNCT
ejpam-2985	416	1	journal	journal	PROPN
ejpam-2985	416	2	of	of	ADP
ejpam-2985	416	3	nonlinear	nonlinear	PROPN
ejpam-2985	416	4	sciences	sciences	PROPN
ejpam-2985	416	5	and	and	CCONJ
ejpam-2985	416	6	applications	application	NOUN
ejpam-2985	416	7	,	,	PUNCT
ejpam-2985	416	8	2(3):161–167	2(3):161–167	NUM
ejpam-2985	416	9	,	,	PUNCT
ejpam-2985	416	10	2009	2009	NUM
ejpam-2985	416	11	.	.	PUNCT
ejpam-2985	417	1	[	[	X
ejpam-2985	417	2	14	14	NUM
ejpam-2985	417	3	]	]	X
ejpam-2985	417	4	r	r	NOUN
ejpam-2985	417	5	kannan	kannan	PROPN
ejpam-2985	417	6	.	.	PUNCT
ejpam-2985	418	1	some	some	DET
ejpam-2985	418	2	results	result	NOUN
ejpam-2985	418	3	on	on	ADP
ejpam-2985	418	4	fixed	fix	VERB
ejpam-2985	418	5	points	point	NOUN
ejpam-2985	418	6	.	.	PUNCT
ejpam-2985	419	1	bulletin	bulletin	NOUN
ejpam-2985	419	2	of	of	ADP
ejpam-2985	419	3	calcutta	calcutta	PROPN
ejpam-2985	419	4	mathematical	mathematical	ADJ
ejpam-2985	419	5	society	society	NOUN
ejpam-2985	419	6	,	,	PUNCT
ejpam-2985	419	7	60:71–76	60:71–76	NUM
ejpam-2985	419	8	,	,	PUNCT
ejpam-2985	419	9	1968	1968	NUM
ejpam-2985	419	10	.	.	PUNCT
ejpam-2985	420	1	[	[	X
ejpam-2985	420	2	15	15	NUM
ejpam-2985	420	3	]	]	X
ejpam-2985	420	4	r	r	NOUN
ejpam-2985	420	5	kannan	kannan	PROPN
ejpam-2985	420	6	.	.	PUNCT
ejpam-2985	421	1	some	some	DET
ejpam-2985	421	2	results	result	NOUN
ejpam-2985	421	3	on	on	ADP
ejpam-2985	421	4	fixed	fix	VERB
ejpam-2985	421	5	points	point	NOUN
ejpam-2985	421	6	ii	ii	PROPN
ejpam-2985	421	7	.	.	PUNCT
ejpam-2985	422	1	american	american	PROPN
ejpam-2985	422	2	mathematics	mathematics	PROPN
ejpam-2985	422	3	monthly	monthly	ADV
ejpam-2985	422	4	,	,	PUNCT
ejpam-2985	422	5	76:405	76:405	PROPN
ejpam-2985	422	6	–	–	PUNCT
ejpam-2985	422	7	408	408	NUM
ejpam-2985	422	8	,	,	PUNCT
ejpam-2985	422	9	1969	1969	NUM
ejpam-2985	422	10	.	.	PUNCT
ejpam-2985	423	1	[	[	X
ejpam-2985	423	2	16	16	NUM
ejpam-2985	423	3	]	]	X
ejpam-2985	423	4	s	s	PART
ejpam-2985	423	5	patil	patil	PROPN
ejpam-2985	423	6	and	and	CCONJ
ejpam-2985	423	7	j	j	PROPN
ejpam-2985	423	8	salunke	salunke	PROPN
ejpam-2985	423	9	.	.	PUNCT
ejpam-2985	424	1	fixed	fix	VERB
ejpam-2985	424	2	point	point	NOUN
ejpam-2985	424	3	theorems	theorem	NOUN
ejpam-2985	424	4	for	for	ADP
ejpam-2985	424	5	expansion	expansion	NOUN
ejpam-2985	424	6	mappings	mapping	NOUN
ejpam-2985	424	7	in	in	ADP
ejpam-2985	424	8	cone	cone	NOUN
ejpam-2985	424	9	rectangular	rectangular	ADJ
ejpam-2985	424	10	metric	metric	ADJ
ejpam-2985	424	11	spaces	space	NOUN
ejpam-2985	424	12	.	.	PUNCT
ejpam-2985	425	1	general	general	ADJ
ejpam-2985	425	2	mathematics	mathematics	PROPN
ejpam-2985	425	3	notes	note	NOUN
ejpam-2985	425	4	,	,	PUNCT
ejpam-2985	425	5	29(1):30–39	29(1):30–39	NUM
ejpam-2985	425	6	,	,	PUNCT
ejpam-2985	425	7	2015	2015	NUM
ejpam-2985	425	8	.	.	PUNCT
ejpam-2985	426	1	[	[	X
ejpam-2985	426	2	17	17	NUM
ejpam-2985	426	3	]	]	X
ejpam-2985	426	4	r	r	NOUN
ejpam-2985	426	5	rashwan	rashwan	NOUN
ejpam-2985	426	6	and	and	CCONJ
ejpam-2985	426	7	s	s	VERB
ejpam-2985	426	8	saleh	saleh	NOUN
ejpam-2985	426	9	.	.	PUNCT
ejpam-2985	427	1	some	some	DET
ejpam-2985	427	2	fixed	fix	VERB
ejpam-2985	427	3	point	point	NOUN
ejpam-2985	427	4	theorems	theorem	NOUN
ejpam-2985	427	5	in	in	ADP
ejpam-2985	427	6	cone	cone	NOUN
ejpam-2985	427	7	rectangular	rectangular	ADJ
ejpam-2985	427	8	metric	metric	ADJ
ejpam-2985	427	9	spaces	space	NOUN
ejpam-2985	427	10	.	.	PUNCT
ejpam-2985	428	1	mathematica	mathematica	PROPN
ejpam-2985	428	2	aeterna	aeterna	PROPN
ejpam-2985	428	3	,	,	PUNCT
ejpam-2985	428	4	2(6):573–587	2(6):573–587	NUM
ejpam-2985	428	5	,	,	PUNCT
ejpam-2985	428	6	2012	2012	NUM
ejpam-2985	428	7	.	.	PUNCT
ejpam-2985	429	1	[	[	X
ejpam-2985	429	2	18	18	NUM
ejpam-2985	429	3	]	]	X
ejpam-2985	429	4	m	m	VERB
ejpam-2985	429	5	reddy	reddy	PROPN
ejpam-2985	429	6	and	and	CCONJ
ejpam-2985	429	7	m	m	PROPN
ejpam-2985	429	8	rangamma	rangamma	NOUN
ejpam-2985	429	9	.	.	PUNCT
ejpam-2985	430	1	a	a	DET
ejpam-2985	430	2	common	common	ADJ
ejpam-2985	430	3	fixed	fix	VERB
ejpam-2985	430	4	point	point	NOUN
ejpam-2985	430	5	theorem	theorem	VERB
ejpam-2985	430	6	for	for	ADP
ejpam-2985	430	7	two	two	NUM
ejpam-2985	430	8	self	self	NOUN
ejpam-2985	430	9	maps	map	NOUN
ejpam-2985	430	10	in	in	ADP
ejpam-2985	430	11	a	a	DET
ejpam-2985	430	12	cone	cone	NOUN
ejpam-2985	430	13	rectangular	rectangular	ADJ
ejpam-2985	430	14	metric	metric	ADJ
ejpam-2985	430	15	space	space	NOUN
ejpam-2985	430	16	.	.	PUNCT
ejpam-2985	431	1	bulletin	bulletin	NOUN
ejpam-2985	431	2	of	of	ADP
ejpam-2985	431	3	mathematics	mathematic	NOUN
ejpam-2985	431	4	and	and	CCONJ
ejpam-2985	431	5	statistics	statistic	NOUN
ejpam-2985	431	6	research	research	NOUN
ejpam-2985	431	7	,	,	PUNCT
ejpam-2985	431	8	3(1):47–53	3(1):47–53	NUM
ejpam-2985	431	9	,	,	PUNCT
ejpam-2985	431	10	2015	2015	NUM
ejpam-2985	431	11	.	.	PUNCT
ejpam-2985	432	1	[	[	X
ejpam-2985	432	2	19	19	NUM
ejpam-2985	432	3	]	]	SYM
ejpam-2985	432	4	s	s	X
ejpam-2985	432	5	rezapour	rezapour	NOUN
ejpam-2985	432	6	and	and	CCONJ
ejpam-2985	432	7	r	r	NOUN
ejpam-2985	432	8	hamlbarani	hamlbarani	NOUN
ejpam-2985	432	9	.	.	PUNCT
ejpam-2985	433	1	some	some	DET
ejpam-2985	433	2	notes	note	NOUN
ejpam-2985	433	3	on	on	ADP
ejpam-2985	433	4	the	the	DET
ejpam-2985	433	5	paper	paper	NOUN
ejpam-2985	433	6	cone	cone	NOUN
ejpam-2985	433	7	metric	metric	ADJ
ejpam-2985	433	8	spaces	space	NOUN
ejpam-2985	433	9	and	and	CCONJ
ejpam-2985	433	10	fixed	fix	VERB
ejpam-2985	433	11	point	point	NOUN
ejpam-2985	433	12	theorems	theorem	NOUN
ejpam-2985	433	13	of	of	ADP
ejpam-2985	433	14	contractive	contractive	ADJ
ejpam-2985	433	15	mappings	mapping	NOUN
ejpam-2985	433	16	.	.	PUNCT
ejpam-2985	434	1	journal	journal	PROPN
ejpam-2985	434	2	of	of	ADP
ejpam-2985	434	3	mathematical	mathematical	ADJ
ejpam-2985	434	4	analysis	analysis	NOUN
ejpam-2985	434	5	and	and	CCONJ
ejpam-2985	434	6	applications	application	NOUN
ejpam-2985	434	7	,	,	PUNCT
ejpam-2985	434	8	345(2):719–724	345(2):719–724	NUM
ejpam-2985	434	9	,	,	PUNCT
ejpam-2985	434	10	2008	2008	NUM
ejpam-2985	434	11	.	.	PUNCT